Stopping functions for grouping and differentiating files based on content

ABSTRACT

Methods and apparatus teach a digital spectrum of a data file. The digital spectrum is used to map a file&#39;s position in multi-dimensional space. This position relative to another file&#39;s position reveals closest neighbors. Certain of the closest neighbors are grouped together, while others are differentiated. Grouping ceases upon application of a stopping function so that rightly sized, optimum numbers of file groups are obtained. Embodiments of stopping functions relate to curve types in a mapping of numbers of groups per sequential rounds of grouping, recognizing whether groups have overlapping file members or not, and/or determining whether groups meet predetermined numbers of members, to name a few. Properly grouped files can then be further acted upon.

This utility application claims priority to U.S. Provisional ApplicationSer. Nos. 61/236,571 and 61/271,079, filed Aug. 25, 2009, and Jul. 16,2009, respectively. Their contents are expressly incorporated herein asif set forth herein.

FIELD OF THE INVENTION

The present invention relates generally to compression/decompression ofdata. More particularly, it relates to defining a digital spectrum of adata file, such as a compressed file, iii order to determine propertiesthat can be compared to other files. In this manner, file similarity,file adjacency and file grouping, to name a few, can be determined.Functions that stop grouping are also examined.

BACKGROUND OF THE INVENTION

Recent data suggests that nearly eighty-five percent of all data isfound in computing files and growing annually at around sixty percent.One reason for the growth is that regulatory compliance acts, statutes,etc., (e.g., Sarbanes-Oxley, HIPAA, PCI) force companies to keep filedata in an accessible state for extended periods of time. However, blocklevel operations in computers are too lowly to apply any meaningfulinterpretation of this stored data beyond taking snapshots and blockde-duplication. While other business intelligence products have beenintroduced to provide capabilities greater than block-level operations,they have been generally limited to structured database analysis. Theyare much less meaningful when acting upon data stored in unstructuredenvironments.

Unfortunately, entities the world over have paid enormous sums of moneyto create and store their data, but cannot find much of it later ininstances where it is haphazardly arranged or arranged less thanintuitively. Not only would locating this information bring back value,but being able to observe patterns in it might also prove valuabledespites its usefulness being presently unknown. However, entitiescannot expend so much time and effort in finding this data that itoutweighs its usefulness. Notwithstanding this, there are still otherscenarios, such as government compliance, litigation, audits, etc., thatdictate certain data/information be found and produced, regardless ofits cost in time, money and effort. Thus, a clear need is identified inthe art to better find, organize and identify digital data, especiallydata left in unstructured states.

In search engine technology, large amounts of unrelated and unstructureddigital data can be quickly gathered. However, most engines do little toorganize the data other than give a hierarchical presentation. Also,when the engine finds duplicate versions of data, it offers few to nooptions on eliminating the replication or migrating/relocatingredundancies. Thus, a further need in the art exists to overcome thedrawbacks of search engines.

When it comes to large amounts of data, whether structured or not,compression techniques have been devised to preserve storage capacity,reduce bandwidth during transmission, etc. With modern compressionalgorithms, however, they simply exist to scrunch large blocks of datainto smaller blocks according to their advertised compression ratios. Asis known, some do it without data loss (lossless) while others do it“lossy.” None do it, unfortunately, with a view toward recognizingsimilarities in the data itself.

From biology, it is known that highly similar species have highlysimilar DNA strings. In the computing context, consider two wordprocessing files relating to stored baseball statistics. In a firstfile, words might appear for a baseball hatter, such as “battingaverage.” “on base percentage,” and “slugging percentage.” while asecond file might have words for a baseball pitcher, such as“strikeouts,” “walks.” and “earned runs.” Conversely, a third filewholly unrelated to baseball, statistics or sports, may have words suchas “environmental protection,” “furniture,” or whatever comes to mind.It would be exceptionally useful if, during times of compression, orupon later manipulation by an algorithm if “mapping” could recognize thesimilarity in subject matter in the first two files, although not exactto one another, and provide options to a user. Appreciating that the“words” in the example files are represented in the computing context asbinary bits (1's or 0's), which occurs by converting the Englishalphabet into a series of 1's and 0's through application of ASCIIencoding techniques, it would be further useful if the compressionalgorithm could first recognize the similarity in subject matter of thefirst two files at the level of raw bit data. The reason for this isthat not all files have words and instead might represent pictures(e.g., .jpeg) or spread sheets of numbers.

Appreciating that certain products already exist in the above-identifiedmarket space, clarity on the need in the art is as follows. One, presentday “keyword matching” is limited to select set of words that have beenpulled from a document into an index for matching to the same exactwords elsewhere. Two, “Grep” is a modern day technique that searches oneor more input files for lines containing an identical match to aspecified pattern. Three. “Beyond Compare,” and similar algorithms, areline-by-line comparisons of multiple documents that highlightdifferences between them. Four, block level data de-duplication has noapplication in compliance contexts, data relocation, or businessintelligence.

The need in the art, on the other hand, needs to serve advanced notionsof identifying new business intelligence, conducting operations oncompletely unstructured or haphazard data, and organizing it, providingnew useful options to users, providing new user views, providing newencryption products, and identifying highly similar data, to name a few.As a byproduct, solving this need will create new opportunities inminimizing transmission bandwidth and storage capacity, among otherthings. Naturally, any improvements along such lines should contemplategood engineering practices, such as stability, ease of implementation,unobtrusiveness, etc.

SUMMARY OF THE INVENTION

The foregoing and other problems are solved by applying the principlesand teachings associated with stopping functions for grouping anddifferentiating files based on underlying content. Broadly, embodimentsof the invention identify self-organizing, emergent patterns in datasets without any keyword, semantic, or metadata processing. Amongcertain advantages is that right number and right sized relevancy groupsfor arbitrary set of data files are readily determined. These relevancygroups are then used to partition a file's underlying data intomeaningful groups without any prior or pre-declared conditions. Humansare also able to easily understand the relationships, but withoutrequired intervention. The files can be of any type as can theirunderlying content.

In representative embodiments, methods and apparatus teach a digitalspectrum of a data file. The digital spectrum is used to map a file'sposition in multi-dimensional space. This position relative to anotherfile's position reveals closest neighbors, among other things. Certainof the closest neighbors are grouped together, while others aredifferentiated from one another. Grouping together continues untilapplication of a stopping function so that rightly sized, optimumnumbers of file groups are obtained. Embodiments of stopping functionsrelate to curve types in a mapping of numbers of groups per sequentialrounds of grouping, recognizing whether groups have overlapping filemembers or not, and/or determining whether groups meet a predeterminedthreshold number of members, to name a few.

In more particular embodiments, curve types can include shapes ofcurves, local minimums and hard stopping points based on numbers ofrounds. Notions of file overlap examine which files exist in whichgroups, while predetermined thresholds of numbers examine variablepercentages of members relative to possible totals. In a computingcontext, files are stored on one or more computing devices. Asrepresentatively encoded, they have pluralities of symbols representingan underlying data stream of original bits of data. These symbols definethe multi-dimensional space in which file positions are examinedrelative to one another. Distances between the files in this space andmatrix sorts of the distances are still other embodiments that areultimately used to facilitate file grouping/differentiating, and thenthe stopping functions.

Executable instructions loaded on one or more computing devices forundertaking the foregoing are also contemplated as are computer programproducts available as a download or on a computer readable medium. Thecomputer program products are also available for installation on anetwork appliance or an individual computing device.

These and other embodiments of the present invention will be set forthin the description which follows, and in part will become apparent tothose of ordinary skill in the art by reference to the followingdescription of the invention and referenced drawings or by practice ofthe invention. The claims, however, indicate the particularities of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings incorporated in and forming a part of thespecification, illustrate several aspects of the present invention, andtogether with the description serve to explain the principles of theinvention. In the drawings:

FIG. 1 is a table in accordance with the present invention showingterminology;

FIG. 2 a table in accordance with the present invention showing a tuplearray and tuple nomenclature;

FIG. 3 is a table in accordance with the present invention showing thecounting of tuples in a data stream;

FIG. 4 is a table in accordance with the present invention showing theCount from FIG. 3 in array form;

FIG. 5 is Pythagorean's Theorem for use in resolving ties in the countsof highest occurring tuples;

FIG. 6 is a table in accordance with the present invention showing arepresentative resolution of a tie in the counts of three highestoccurring tuples using Pythagorean's Theorem;

FIG. 7 is a table in accordance with the present invention showing analternative resolution of a tie in the counts of highest occurringtuples;

FIG. 8 is an initial dictionary in accordance with the present inventionfor the data stream of FIG. 9;

FIGS. 8-60 are iterative data streams and tables in accordance with thepresent invention depicting dictionaries, arrays, tuple counts,encoding, and the like illustrative of multiple passes through thecompression algorithm;

FIG. 61 is a chart in accordance with the present invention showingcompression optimization;

FIG. 62 is a table in accordance with the present invention showingcompression statistics;

FIGS. 63-69 are diagrams and tables in accordance with the presentinvention relating to storage of a compressed file;

FIGS. 70-82 b are data streams, tree diagrams and tables in accordancewith the present invention relating to decompression of a compressedfile;

FIG. 83 is a diagram in accordance with the present invention showing arepresentative computing device for practicing all or some theforegoing;

FIGS. 84-93 are diagrams in accordance with a “fast approximation”embodiment of the invention that utilizes key information of an earliercompressed file for a file under present consideration having patternssubstantially similar to the earlier compressed file;

FIGS. 94-98A-B are definitions and diagrams in accordance with thepresent invention showing a “digital spectrum” embodiment of an encodedfile, including grouping of files; and

FIGS. 99A-99B, 100A-100B and 101-105 are diagrams, graphs and flowcharts in accordance with the present invention for grouping anddifferentiating files and determining stopping functions duringgrouping.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

In the following detailed description of the illustrated embodiments,reference is made to the accompanying drawings that form a part hereof,and in which is shown by way of illustration, specific embodiments inwhich the invention may be practiced. These embodiments are described insufficient detail to enable those skilled in the art to practice theinvention and like numerals represent like details in the variousfigures. Also, it is to be understood that other embodiments may beutilized and that process, mechanical, electrical, arrangement, softwareand/or other changes may be made without departing from the scope of thepresent invention. In accordance with the present invention, methods andapparatus are hereinafter described for optimizing data compression ofdigital data.

In a representative embodiment, compression occurs by finding highlyoccurring patterns in data streams, and replacing them with newlydefined symbols that require less space to store than the originalpatterns. The goal is to eliminate as much redundancy from the digitaldata as possible. The end result has been shown by the inventor toachieve greater compression ratios on certain tested files thanalgorithms heretofore known.

In information theory, it is well understood that collections of datacontain significant amounts of redundant information. Some redundanciesare easily recognized, while others are difficult to observe. A familiarexample of redundancy in the English language is the ordered pair ofletters QU. When Q appears in written text, the reader anticipates andexpects the letter U to follow, such as in the words queen, quick,acquit, and square. The letter U is mostly redundant information when itfollows Q. Replacing a recurring pattern of adjacent characters with asingle symbol can reduce the amount of space that it takes to store thatinformation. For example, the ordered pair of letters QU can be replacedwith a single memorable symbol when the text is stored. For thisexample, the small Greek letter alpha (α) is selected as the symbol, butany could be chosen that does not otherwise appear in the text underconsideration. The resultant compressed text is one letter shorter foreach occurrence of QU that is replaced with the single symbol (α), e.g.,“αeen,” “αick,” “acαit,” and “sαare.” Such is also stored with adefinition of the symbol alpha (α) in order to enable the original datato be restored. Later, the compressed text can be expanded by replacingthe symbol with the original letters QU. There is no information loss.Also, this process can be repeated many times over to achieve furthercompression.

DEFINITIONS

With reference to FIG. 1, a table 10 is used to define terminology usedin the below compression method and procedure.

Discussion

Redundancy is the superfluous repetition of information. As demonstratedin the QU example above, adjacent characters in written text often formexpected patterns that are easily detected. In contrast, digital data isstored as a series of bits where each bit can have only one of twovalues: off (represented as a zero (0)) and on (represented as a one(1)). Redundancies in digital data, such as long sequences of zeros orones, are easily seen with the human eye. However, patterns are notobvious in highly complex digital data. The invention's methods andprocedures identify these redundancies in stored information so thateven highly complex data can be compressed. In turn, the techniques canbe used to reduce, optimize, or eliminate redundancy by substituting theredundant information with symbols that take less space to store thanthe original information. When it is used to eliminate redundancy, themethod might originally return compressed data that is larger than theoriginal. This can occur because information about the symbols and howthe symbols are encoded for storage must also be stored so that the datacan be decompressed later. For example, compression of the word “queen”above resulted in the compressed word “αeen.” But a dictionary havingthe relationship QU=αalso needed to be stored with the word “αeen,”which makes a “first pass” through the compression technique increase insize, not decrease. Eventually, however, further “passes” will stopincreasing and decrease so rapidly, despite the presence of anever-growing dictionary size, that compression ratios will be shown togreatly advance the state of the art. By automating the techniques withcomputer processors and computing software, compression will also occurexceptionally rapidly. In addition, the techniques herein will be shownto losslessly compress the data.

The Compression Procedure

The following compression method iteratively substitutes symbols forhighly occurring tuples in a data stream. An example of this process isprovided later in the document.

Prerequisites

The compression procedure will be performed on digital data. Each storedbit has a value of binary 0 or binary 1. This series of bits is referredto as the original digital data.

Preparing the Data

The original digital data is examined at the bit level. The series ofbits is conceptually converted to a stream of characters, referred to asthe data stream that represents the original data. The symbols 0 and 1are used to represent the respective raw bit values in the new datastream. These symbols are considered to be atomic because allsubsequently defined symbols represent tuples that are based on 0 and 1.

A dictionary is used to document the alphabet of symbols that are usedin the data stream. Initially, the alphabet consists solely of thesymbols 0 and 1.

Compressing the Data Stream

The following tasks are performed iteratively on the data stream:

-   -   Identifying all possible tuples that can occur for the set of        characters that are in the current data stream.    -   Determining which of the possible tuples occurs most frequently        in the current data stream. In the case of a tie, use the most        complex tuple. (Complexity is discussed below.)    -   Creating a new symbol for the most highly occurring tuple, and        add it to the dictionary.    -   Replacing all occurrences of the most highly occurring tuple        with the new symbol.    -   Encoding the symbols in the data stream by using an encoding        scheme, such as a path-weighted Huffman coding scheme.    -   Calculating the compressed file size.    -   Determining whether the compression goal has been achieved.    -   Repeating for as long as necessary to achieve optimal        compression. That is, if a stream of data were compressed so        completely that it was represented by a single bit, it and its        complementary dictionary would be larger than the original        representation of the stream of data absent the compression.        (For example, in the QU example above, if “α” represented the        entire word “queen,” the word “queen” could be reduced to one        symbol, e.g., “α.” However, this one symbol and its dictionary        (reciting “queen=α” is larger than the original content        “queen.”) Thus, optimal compression herein recognizes a point of        marginal return whereby the dictionary grows too large relative        to the amount of compression being achieved by the technique.        Each of these steps is described in more detail below.        Identifying all Possible Tuples

From FIG. 1, a “tuple” is an ordered pair of adjoining characters in adata stream. To identify all possible tuples in a given data stream, thecharacters in the current alphabet are systematically combined to formordered pairs of symbols. The left symbol in the pair is referred to asthe “first” character, while the right symbol is referred to as the“last” character. In a larger context, the tuples represent the“patterns” examined in a data stream that will yield further advantagein the art.

In the following example and with any data stream of digital data thatcan be compressed according to the techniques herein, two symbols (0and 1) occur in the alphabet and are possibly the only symbols in theentire data stream. By examining them as “tuples,” the combination ofthe 0 and 1 as ordered pairs of adjoining characters reveals only fourpossible outcomes, i.e., a tuple represented by “00,” a tuplerepresented by “01,” a tuple represented by “10,” and a tuplerepresented by “11.”

With reference to FIG. 2, these four possibilities are seen in table 12.In detail, the table shows the tuple array for characters 0 and 1. Inthe cell for column 0 and row 0, the tuple is the ordered pair of 0followed by 0. The shorthand notation of the tuple in the first cell is“0>0”. In the cell for column 0 and row 1, the tuple is 0 followed by 1,or “0>1”. In the cell for column 1 and row 0, the tuple is “1>0”. In thecell for column 1 and row 1, the tuple is “1>1”.

Determining the Most Highly Occurring Tuple

With FIG. 2 in mind, it is determined which tuple in a bit stream is themost highly occurring. To do this, simple counting occurs. It revealshow many times each of the possible tuples actually occurs. Each pair ofadjoining characters is compared to the possible tuples and the count isrecorded for the matched tuple.

The process begins by examining the adjacent characters in position oneand two of the data stream. Together, the pair of characters forms atuple. Advance by one character in the stream and examine the charactersin positions two and three. By incrementing through the data stream onecharacter at a time, every combination of two adjacent characters in thedata stream is examined and tallied against one of the tuples.

Sequences of repeated symbols create a special case that must beconsidered when tallying tuples. That is, when a symbol is repeatedthree or more times, skilled artisans might identify instances of atuple that cannot exist because the symbols in the tuple belong to otherinstances of the same tuple. The number of actual tuples in this case isthe number of times the symbol repeats divided by two.

For example, consider the data stream 14 in table 16 (FIG. 3) having 10characters shown as “0110000101.” Upon examining the first twocharacters 01, a tuple is recognized in the form 0 followed by 1 (0>1).Then, increment forward one character and consider the second and thirdcharacters 11, which forms the tuple of 1 followed by 1 (1>1). Asprogression occurs through the data stream, 9 possible tuplecombinations are found: 0>1, 1>1, 1>0, 0>0, 0>0, 0>0, 0>1, 1>0, and 0>1(element 15, FIG. 3). In the sequence of four sequential zeros (at thefourth through seventh character positions in the data stream“0110000101”), three instances of a 0 followed by a 0 (or 0>0) areidentified as possible tuples. It is observed that the second instanceof the 0>0 tuple (element 17, FIG. 3) cannot be formed because thesymbols are used in the 0>0 tuple before and after it, by prescribedrule. Thus, there are only two possible instances in the COUNT 18, FIG.3, of the 0>0 tuple, not 3. In turn, the most highly occurring tuplecounted in this data stream is 0>1, which occurs 3 times (element 19,FIG. 3). Similarly, tuple 1>1 occurs once (element 20, FIG. 3), whiletuple 1>0 occurs twice (element 21, FIG. 3).

After the entire data stream has been examined, the final counts foreach tuple are compared to determine which tuple occurs most frequently.In tabular form, the 0 followed by a 1 (tuple 0>1) occurs the most andis referenced at element 19 in table 22, FIG. 4.

In the situation of a tie between two or more tuples, skilled artisansmust choose between one of the tuples. For this, experimentation hasrevealed that choosing the tuple that contains the most complexcharacters usually results in the most efficient compression. If alltuples are equally complex, skilled artisans can choose any one of thetied tuples and define it as the most highly occurring.

The complexity of a tuple is determined by imagining that the symbolsform the sides of a right triangle, and the complexity is a measure ofthe length of the hypotenuse of that triangle. Of course, the hypotenuseis related to the sum of the squares of the sides, as defined by thePythagorean Theorem, FIG. 5.

The tuple with the longest hypotenuse is considered the most complextuple, and is the winner in the situation of a tie between the highestnumbers of occurring tuples. The reason for this is that less-complextuples in the situation of a tie are most likely to be resolved insubsequent passes in the decreasing order of their hypotenuse length.Should a tie in hypotenuse length occur, or a tie in complexity,evidence appears to suggest it does not make a difference which tuple ischosen as the most highly occurring.

For example, suppose that tuples 3>7, 4>4 and 1>5 each occur 356 timeswhen counted (in a same pass). To determine the complexity of eachtuple, use the tuple symbols as the two sides of a right triangle andcalculate the hypotenuse, FIG. 6. In the instance of 3>7, the side ofthe hypotenuse is the square root of (three squared (9) plus sevensquared (49)), or the square root of 58, or 7.6. In the instance of 4>4,the side of the hypotenuse is the square root of (four squared (16) plusfour squared (16), of the square root of 32, or 5.7. Similar, 1>5calculates as a hypotenuse of 5.1 as seen in table 23 in the Figure.Since the tuple with the largest hypotenuse is the most complex, 3>7'shypotenuse of 7.6 is considered more complex than either of the tuples4>4 or 1>5.

Skilled artisans can also use the tuple array to visualize thehypotenuse by drawing lines in the columns and rows from the arrayorigin to the tuple entry in the array, as shown in table 24 in FIG. 7.As seen, the longest hypotenuse is labeled 25, so the 3>7 tuple wins thetie, and is designated as the most highly occurring tuple. Hereafter, anew symbol is created to replace the highest occurring tuple (whetheroccurring the most outright by count or by tie resolution), as seenbelow. However, based on the complexity rule, it is highly likely thatthe next passes will replace tuple 4>4 and then tuple

Creating a Symbol for the Most Highly Occurring Tuple

As before, a symbol stands for the two adjacent characters that form thetuple and skilled artisans select any new symbol they want provided itis not possibly found in the data stream elsewhere. Also, since thesymbol and its definition are added to the alphabet, e.g., if “α=QU,” adictionary grows by one new symbol in each pass through the data, aswill be seen. A good example of a new symbol for use in the invention isa numerical character, sequentially selected, because numbers provide anunlimited source of unique symbols. In addition, reaching an optimizedcompression goal might take thousands (or even tens of thousands) ofpasses through the data stream and redundant symbols must be avoidedrelative to previous passes and future passes.

Replacing the Tuple with the New Symbol

Upon examining the data stream to find all occurrences of the highestoccurring tuple, skilled artisans simply substitute the newly defined ornewly created symbol for each occurrence of that tuple. Intuitively,substituting a single symbol for two characters compresses the datastream by one character for each occurrence of the tuple that isreplaced.

Encoding the Alphabet

To accomplish this, counting occurs for how many times that each of thesymbols in the current alphabet occurs in the data stream. They then usethe symbol count to apply an encoding scheme, such as a path-weightedHuffman coding scheme, to the alphabet. Huffman trees should be withinthe purview of the artisan's skill set.

The encoding assigns bits to each symbol in the current alphabet thatactually appears in the data stream. That is, symbols with a count ofzero occurrences are not encoded in the tree. Also, symbols might go“extinct” in the data stream as they are entirely consumed by yet morecomplex symbols, as will be seen. As a result, the Huffman code tree isrebuilt every time a new symbol is added to the dictionary. This meansthat the Huffman code for a given symbol can change with every pass. Theencoded length of the data stream usually decreases with each pass.

Calculating the Compressed File Size

The compressed file size is the total amount of space that it takes tostore the Huffman-encoded data stream plus the information about thecompression, such as information about the file, the dictionary, and theHuffman encoding tree. The compression information must be saved alongwith other information so that the encoded data can be decompressedlater.

To accomplish this, artisans count the number of times that each symbolappears in the data stream. They also count the number of bits in thesymbol's Huffman code to find its bit length. They then multiply the bitlength by the symbol count to calculate the total bits needed to storeall occurrences of the symbol. This is then repeated for each symbol.Thereafter, the total bit counts for all symbols are added to determinehow many bits are needed to store only the compressed data. To determinethe compressed file size, add the total bit count for the data to thenumber of bits required for the related compression information (thedictionary and the symbol-encoding information).

Determining Whether the Compression Goal has been Achieved

Substituting a tuple with a single symbol reduces the total number ofcharacters in a data stream by one for each instance of a tuple that isreplaced by a symbol. That is, for each instance, two existingcharacters are replaced with one new character. In a given pass, eachinstance of the tuple is replaced by a new symbol. There are threeobserved results:

-   -   The length of the data stream (as measured by how many        characters make up the text) decreases by half the number of        tuples replaced.    -   The number of symbols in the alphabet increases by one.    -   The number of nodes in the Huffman tree increases by two.

By repeating the compression procedure a sufficient number of times, anyseries of characters can eventually be reduced to a single character.That “super-symbol” character conveys the entire meaning of the originaltext. However, the information about the symbols and encoding that isused to reach that final symbol is needed to restore the original datalater. As the number of total characters in the text decreases with eachrepetition of the procedure, the number of symbols increases by one.With each new symbol, the size of the dictionary and the size of theHuffman tree increase, while the size of the data decreases relative tothe number of instances of the tuple it replaces. It is possible thatthe information about the symbol takes more space to store than theoriginal data it replaces. In order for the compressed file size tobecome smaller than the original data stream size, the text size mustdecrease faster than the size increases for the dictionary and theHuffman encoding information.

The question at hand is then, what is the optimal number ofsubstitutions (new symbols) to make, and how should those substitutionsbe determined?

For each pass through the data stream, the encoded length of the textdecreases, while the size of the dictionary and the Huffman treeincreases. It has been observed that the compressed file size will reacha minimal value, and then increase. The increase occurs at some pointbecause so few tuple replacements are done that the decrease in textsize no longer outweighs the increase in size of the dictionary andHuffman tree.

The size of the compressed file does not decrease smoothly or steadilydownward. As the compression process proceeds, the size might plateau ortemporarily increase. In order to determine the true (global) minimum,it is necessary to continue some number of iterations past the each new(local) minimum point. This true minimal value represents the optimalcompression for the data stream using this method.

Through experimentation, three conditions have been found that can beused to decide when to terminate the compression procedure: asymptoticreduction, observed low, and single character. Each method is describedbelow. Other terminating conditions might be determined through furtherexperimentation.

Asymptotic Reduction

An asymptotic reduction is a concession to processing efficiency, ratherthan a completion of the procedure. When compressing larger files (100kilobytes (KB) or greater), after several thousand passes, eachadditional pass produces only a very small additional compression. Thecompressed size is still trending downward, but at such a slow rate thatadditional compute time is not warranted.

Based on experimental results, the process is terminated if at least1000 passes have been done, and less than 1% of additional data streamcompression has occurred in the last 1000 passes. The previously notedminimum is therefore used as the optimum compressed file.

Observed Low

A reasonable number of passes have been performed on the data and in thelast reasonable number of passes a new minimum encoded file size has notbeen detected. It appears that further passes only result in a largerencoded file size.

Based on experimental results, the process is terminated if at least1000 passes have been done, and in the last 10% of the passes, a new lowhas not been established. The previously noted minimum is then used asthe optimum compressed file.

Single Character

The data stream has been reduced to exactly one character. This caseoccurs if the file is made up of data that can easily reduce to a singlesymbol, such a file filled with a repeating pattern. In cases like this,compression methods other than this one might result in smallercompressed file sizes.

How the Procedure Optimizes Compression

The representative embodiment of the invention uses Huffman trees toencode the data stream that has been progressively shortened by tuplereplacement, and balanced against the growth of the resultant Huffmantree and dictionary representation.

The average length of a Huffman encoded symbol depends upon two factors:

-   -   How many symbols must be represented in the Huffman tree    -   The distribution of the frequency of symbol use

The average encoded symbol length grows in a somewhat stepwise fashionas more symbols are added to the dictionary. Because the Huffman tree isa binary tree, increases naturally occur as the number of symbols passeseach level of the power of 2 (2, 4, 8, 16, 32, 64, etc.). At thesepoints, the average number of bits needed to represent any given symbolnormally increases by 1 bit, even though the number of characters thatneed to be encoded decreases. Subsequent compression passes usuallyovercome this temporary jump in encoded data stream length.

The second factor that affects the efficiency of Huffman coding is thedistribution of the frequency of symbol use. If one symbol is usedsignificantly more than any other, it can be assigned a shorter encodingrepresentation, which results in a shorter encoded length overall, andresults in maximum compression. The more frequently a symbol occurs, theshorter the encoded stream that replaces it. The less frequently asymbol occurs, the longer the encoded stream that replaces it.

If all symbols occur at approximately equal frequencies, the number ofsymbols has the greater effect than does the size of the encoded datastream. Supporting evidence is that maximum compression occurs whenminimum redundancy occurs, that is, when the data appears random. Thisstate of randomness occurs when every symbol occurs at the samefrequency as any other symbol, and there is no discernable ordering tothe symbols.

The method and procedure described in this document attempt to create astate of randomness in the data stream. By replacing highly occurringtuples with new symbols, eventually the frequency of all symbols presentin the data stream becomes roughly equal. Similarly, the frequency ofall tuples is also approximately equal. These two criteria (equaloccurrence of every symbol and equal occurrence of ordered symbolgroupings) is the definition of random data. Random data means noredundancy. No redundancy means maximum compression.

This method and procedure derives optimal compression from a combinationof the two factors. It reduces the number of characters in the datastream by creating new symbols to replace highly occurring tuples. Thefrequency distribution of symbol occurrence in the data stream tends toequalize as oft occurring symbols are eliminated during tuplereplacement. This has the effect of flattening the Huffman tree,minimizing average path lengths, and therefore, minimizing encoded datastream length. The number of newly created symbols is held to a minimumby measuring the increase in dictionary size against the decrease inencoded data stream size.

Example of Compression

To demonstrate the compression procedure, a small data file contains thefollowing simple ASCII characters:

aaaaaaaaaaaaaaaaaaaaaaaaaaabaaabaaaaaaaababbbbbb

Each character is stored as a sequence of eight bits that correlates tothe ASCII code assigned to the character. The bit values for eachcharacter are:

a=01100001

b=01100010

The digital data that represents the file is the original data that weuse for our compression procedure. Later, we want to decompress thecompressed file to get back to the original data without data loss.

Preparing the Data Stream

The digital data that represents the file is a series of bits, whereeach bit has a value of 0 or 1. We want to abstract the view of the bitsby conceptually replacing them with symbols to form a sequential streamof characters, referred to as a data stream.

For our sample digital data, we create two new symbols called 0 and 1 torepresent the raw bit values of 0 and 1, respectively. These two symbolsform our initial alphabet, so we place them in the dictionary 26, FIG.8.

The data stream 30 in FIG. 9 represents the original series of bits inthe stored file, e.g., the first eight bits 32 are “01100001” andcorrespond to the first letter “a” in the data file. Similarly, the verylast eight bits 34 are “01100010” and correspond to the final letter “b”in the data file, and each of the 1's and 0's come from the ASCII codeabove.

Also, the characters in data stream 30 are separated with a space foruser readability, but the space is not considered, just the characters.The space would not occur in computer memory either.

Compressing the Data Stream

The data stream 30 of FIG. 9 is now ready for compression. The procedurewill be repeated until the compression goal is achieved. For thisexample, the compression goal is to minimize the amount of space that ittakes to store the digital data.

Initial Pass

For the initial pass, the original data stream and alphabet that werecreated in “Preparing the Data Stream” are obtained.

Identifying all Possible Tuples

An easy way to identify all possible combinations of the characters inour current alphabet (at this time having 0 and 1) is to create a tuplearray (table 35, FIG. 10). Those symbols are placed or fitted as acolumn and row, and the cells are filled in with the tuple that combinesthose symbols. The columns and rows are constructed alphabetically fromleft to right and top to bottom, respectively, according to the orderthat the symbols appear in our dictionary. For this demonstration, wewill consider the symbol in a column to be the first character in thetuple, and the symbol in a row to be the last character in the tuple. Tosimplify the presentation of tuples in each cell, we will use theearlier-described notation of “first>last” to indicate the order ofappearance in the pair of characters, and to make it easier to visuallydistinguish the symbols in the pair. The tuples shown in each cell nowrepresent the patterns we want to look for in the data stream.

For example, the table 35 shows the tuple array for characters 0 and 1.In the cell for column 0 and row 0, the tuple is the ordered pair of 0followed by 0. The shorthand notation of the tuple in the first cell is“0>0”. In the cell for column 0 and row 1, the tuple is 0 followed by 1,or “0>1”. In the cell for column 1 and row 0, the tuple is “1>0”. In thecell for column 1 and row 1, the tuple is “1>1”. (As skilled artisanswill appreciate, most initial dictionaries and original tuple arrayswill be identical to these. The reason is that computing data streamswill all begin with a stream of 1's and 0's having two symbols only.)

Determining the Highly Occurring Tuple

After completion of the tuple array, we are ready to look for the tuplesin the data stream 30, FIG. 9. We start at the beginning of the datastream with the first two characters “01” labeled element 37. We comparethis pair of characters to our known tuples, keeping in mind that ordermatters. We match the pair to a tuple, and add one count for thatinstance. We move forward by one character, and look at the pair ofcharacters 38 in positions two and three in the data stream, or “11.” Wecompare and match this pair to one of the tuples, and add one count forthat instance. We continue tallying occurrences of the tuples in thismanner until we reach the end of the data stream. In this instance, thefinal tuple is “10” labeled 39. By incrementing through the data streamone character at a time, we have considered every combination of twoadjacent characters in the data stream, and tallied each instanceagainst one of the tuples. We also consider the rule for sequences ofrepeated symbols, described above, to determine the actual number ofinstances for the tuple that is defined by pairs of that symbol.

For example, the first two characters in our sample data stream are 0followed by 1. This matches the tuple 0>1, so we count that as oneinstance of the tuple. We step forward one character. The characters inpositions two and three are 1 followed by 1, which matches the tuple1>1. We count it as one instance of the 1>1 tuple. We consider thesequences of three or more zeros in the data stream (e.g., 01100001 . .. ) to determine the actual number of tuples for the 0>0 tuple. Werepeat this process to the end of the data set with the count results intable 40, FIG. 11.

Now that we have gathered statistics for how many times each tupleappears in the data stream 30, we compare the total counts for eachtuple to determine which pattern is the most highly occurring. The tuplethat occurs most frequently is a tie between a 1 followed by 0 (1>0),which occurs 96 times, and a 0 followed by 1 (0>1), which also occurs 96times. As discussed above, skilled artisans then choose the most complextuple and do so according to Pythagorean's Theorem. The sum of thesquares for each tuple is the same, which is 1 (1+0) and 1 (0+1).Because they have the same complexity, it does not matter which one ischosen as the highest occurring. In this example, we will choose tuple1>0.

We also count the number of instances of each of the symbols in thecurrent alphabet as seen in table 41, FIG. 12. The total symbol count inthe data stream is 384 total symbols that represent 384 bits in theoriginal data. Also, the symbol 0 appears 240 times in original datastream 30, FIG. 9, while the symbol 1 only appears 144 times.

Pass 1

In this next pass, we replace the most highly occurring tuple from theprevious pass with a new symbol, and then we determine whether we haveachieved our compression goal.

Creating a Symbol for the Highly Occurring Tuple

We replace the most highly occurring tuple from the previous pass with anew symbol and add it to the alphabet. Continuing the example, we add anew symbol 2 to the dictionary and define it with the tuple defined as 1followed by 0 (1>0). It is added to the dictionary 26′ as seen in FIG.13. (Of course, original symbol 0 is still defined as a 0, whileoriginal symbol 1 is still defined as a 1. Neither of these represent afirst symbol followed a last symbol which is why dashes appear in thedictionary 26′ under “Last” for each of them.)

Replacing the Tuple with the New Symbol

In the original data stream 30, every instance of the tuple 1>0 is nowreplaced with the new, single symbol. In our example data stream 30,FIG. 9, the 96 instances of the tuple 1>0 have been replaced with thenew symbol “2” to create the output data stream 30′, FIG. 14, that wewill use for this pass. As skilled artisans will observe, replacingninety-six double instances of symbols with a single, new symbol shrinksor compresses the data stream 30′ in comparison to the original datastream 30. FIG. 8.

Encoding the Alphabet

After we compress the data stream by using the new symbol, we use apath-weighted Huffman coding scheme to assign bits to each symbol in thecurrent alphabet.

To do this, we again count the number of instances of each of thesymbols in the current alphabet (now having “0.” “1” and “2.”) The totalsymbol count in the data stream is 288 symbols as seen in table 4F, FIG.15. We also have one end-of-file (EOF) symbol at the end of the datastream (not shown).

Next, we use the counts to build a Huffman binary code tree. 1) List thesymbols from highest count to lowest count. 2) Combine the counts forthe two least frequently occurring symbols in the dictionary. Thiscreates a node that has the value of the sum of the two counts. 3)Continue combining the two lowest counts in this manner until there isonly one symbol remaining. This generates a Huffman binary code tree.

Finally, label the code tree paths with zeros (0s) and ones (1s). TheHuffman coding scheme assigns shorter code words to the more frequentsymbols, which helps reduce the size length of the encoded data. TheHuffman code for a symbol is defined as the string of values associatedwith each path transition from the root to the symbol terminal node.

With reference to FIG. 16, the tree 50 demonstrates the process ofbuilding the Huffman tree and code for the symbols in the currentalphabet. We also create a code for the end of file marker that weplaced at the end of the data stream when we counted the tuples. In moredetail, the root contemplates 289 total symbols, i.e., the 288 symbolsfor the alphabet “0.” “1” and “2” plus one EOF symbol. At the leaves,the “0” is shown with its counts 144, the “1” with its count of 48, the“2” with its count of 96 and the EOF with its count of 1. Between theleaves and root, the branches define the count in a manner skilledartisans should readily understand.

In this compression procedure, we will re-build a Huffman code treeevery time we add a symbol to the current dictionary. This means thatthe Huffman code for a given symbol can change with every compressionpass.

Calculating the Compressed File Size

From the Huffman tree, we use its code to evaluate the amount of spaceneeded to store the compressed data as seen in table 52, FIG. 17. First,we count the number of bits in the Huffman code for each symbol to findits bit length 53. Next, we multiply a symbol's bit length by its count54 to calculate the total bits 55 used to store the occurrences of thatsymbol. We add the total bits 56 needed for all symbols to determine howmany bits are needed to store only the compressed data. As seen, thecurrent data stream 30′. FIG. 14 requires 483 bits to store only theinformation.

To know whether we achieved optimal compression, we must consider thetotal amount of space that it takes to store the compressed data plusthe information about the compression that we need to store in order todecompress the data later. We also must store information about thefile, the dictionary, and the Huffman tree. The table 57 in FIG. 18shows the total compression overhead as being 25 bits, which brings thecompressed size of the data stream to 508 bits, or 483 bits plus 25bits.

Determining Whether the Compression Goal has been Achieved

Finally, we compare the original number of bits (384, FIG. 12) to thecurrent number of bits (508) that are needed for this compression pass.We find that it takes 1.32 times as many bits to store the compresseddata as it took to store the original data, table 58, FIG. 19. This isnot compression at all, but expansion.

In early passes, however, we expect to see that the substitutionrequires more space than the original data because of the effect ofcarrying a dictionary, adding symbols, and building a tree. On the otherhand, skilled artisans should observe an eventual reduction in theamount of space needed as the compression process continues. Namely, asthe size of the data set decreases by the symbol replacement method, thesize grows for the symbol dictionary and the Huffman tree informationthat we need for decompressing the data.

Pass 2

In this pass, we replace the most highly occurring tuple from theprevious pass (pass 1) with still another new symbol, and then wedetermine whether we have achieved our compression goal.

Identifying all Possible Tuples

As a result of the new symbol, the tuple array is expanded by adding thesymbol that was created in the previous pass. Continuing our example, weadd 2 as a first symbol and last symbol, and enter the tuples in the newcells of table 35′, FIG. 20.

Determining the Highly Occurring Tuple

As before, the tuple array identifies the tuples that we look for andtally in our revised alphabet. As seen in table 40′. FIG. 21, the TotalSymbol Count=288. The tuple that occurs most frequently when countingthe data stream 30′. FIG. 14, is the character 2 followed by thecharacter 0 (2>0). It occurs 56 times as seen circled in table 40′ FIG.21.

Creating a Symbol for the Highly Occurring Tuple

We define still another new symbol “3” to represent the most highlyoccurring tuple 2>0, and add it to the dictionary 26″, FIG. 22, for thealphabet that was developed in the previous passes.

Replacing the Tuple with the New Symbol

In the data stream 30′. FIG. 14, we replace every instance of the mosthighly occurring tuple with the new single symbol. We replace the 56instances of the 2>0 tuple with the symbol 3 and the resultant datastream 30′″ is seen in FIG. 23.

Encoding the Alphabet

As demonstrated above, we count the number of symbols in the datastream, and use the count to build a Huffman tree and code for thecurrent alphabet. The total symbol count has been reduced from 288 to234 (e.g., 88+48+40+58, but not including the EOF marker) as seen intable 41″, FIG. 24.

Calculating the Compressed File Size

We need to evaluate whether our substitution reduces the amount of spacethat it takes to store the data. As described above, we calculate thetotal bits needed (507) as in table 52′, FIG. 25.

In table 57′. FIG. 26, the compression overhead is calculated as 38bits.

Determining Whether the Compression Goal has been Achieved

Finally, we compare the original number of bits (384) to the currentnumber of bits (545=507+38) that are needed for this compression pass.We find that it takes 141% or 1.41 times as many bits to store thecompressed data as it took to store the original data. Compression isstill not achieved and the amount of data in this technique is growinglarger rather than smaller in comparison to the previous pass requiring132%.

Pass 3

In this pass, we replace the most highly occurring tuple from theprevious pass with a new symbol, and then we determine whether we haveachieved our compression goal.

Identifying all Possible Tuples

We expand the tuple array 35″. FIG. 28 by adding the symbol that wascreated in the previous pass. We add the symbol “3” as a first symboland last symbol, and enter the tuples in the new cells.

Determining the Highly Occurring Tuple

The tuple array identifies the tuples that we look for and tally in ourrevised alphabet. In table 40″, FIG. 29, the Total Symbol Count is 232,and the tuple that occurs most frequently is the character 1 followed bycharacter 3 (1>3). It occurs 48 times, which ties with the tuple ofcharacter 3 followed by character 0. We determine that the tuple 1>3 isthe most complex tuple because it has a hypotenuse length 25′ of 3.16(SQRT(1²+3²)), and tuple 3>0 has a hypotenuse of 3 (SQRT(0²+3²)).

Creating a Symbol for the Highly Occurring Tuple

We define a new symbol 4 to represent the most highly occurring tuple1>3, and add it to the dictionary 26′. FIG. 30, for the alphabet thatwas developed in the previous passes.

Replacing the Tuple with the New Symbol

In the data stream, we replace every instance of the most highlyoccurring tuple from the earlier data stream with the new single symbol.We replace the 48 instances of the 1>3 tuple with the symbol 4 and newdata stream 30-4 is obtained, FIG. 31.

Encoding the Alphabet

We count the number of symbols in the data stream, and use the count tobuild a Huffman tree and code for the current alphabet as seen in table41′″. FIG. 32. There is no Huffman code assigned to the symbol 1 becausethere are no instances of this symbol in the compressed data in thispass. (This can be seen in the data stream 30-4, FIG. 31.) The totalsymbol count has been reduced from 232 to 184 (e.g., 88+0+40+8+48, butnot including the EOF marker).

Calculating the Compressed File Size

We need to evaluate whether our substitution reduces the amount of spacethat it takes to store the data. As seen in table 52″. FIG. 33 the totalbits are equal to 340.

In table 57″. FIG. 34 the compression overhead in bits is 42.

Determining Whether the Compression Goal has been Achieved

Finally, we compare the original number of bits (384) to the currentnumber of bits (382) that are needed for this compression pass. We findthat it takes 0.99 times as many bits to store the compressed data as ittook to store the original data. Compression is achieved.

Pass 4

In this pass, we replace the most highly occurring tuple from theprevious pass with a new symbol, and then we determine whether we haveachieved our compression goal.

Identifying all Possible Tipples

We expand the tuple array 35′″, FIG. 36, by adding the symbol that wascreated in the previous pass. We add the symbol 4 as a first symbol andlast symbol, and enter the tuples in the new cells.

Determining the Highly Occurring Tuple

The tuple array identifies the tuples that we look for and tally in ourrevised alphabet. In table 40′″, FIG. 37, the Total Symbol Count=184 andthe tuple that occurs most frequently is the character 4 followed bycharacter 0 (4>0). It occurs 48 times.

Creating a Symbol for the Highly Occurring Tuple

We define a new symbol 5 to represent the 4>0 tuple, and add it to thedictionary 26-4, FIG. 38, for the alphabet that was developed in theprevious passes.

Replacing the Tuple with the New Symbol

In the data stream, we replace every instance of the most highlyoccurring tuple with the new single symbol. We replace the 48 instancesof the 40 tuple in data stream 30-4, FIG. 31, with the symbol 5 as seenin data stream 30-5, FIG. 39.

Encoding the Alphabet

As demonstrated above, we count the number of symbols in the datastream, and use the count to build a Huffman tree and code for thecurrent alphabet. There is no Huffman code assigned to the symbol 1 andthe symbol 4 because there are no instances of these symbols in thecompressed data in this pass. The total symbol count has been reducedfrom 184 to 136 (e.g., 40+0+40+8+0+48, but not including the EOF marker)as seen in table 41-4, FIG. 40.

Calculating the Compressed File Size

We need to evaluate whether our substitution reduces the amount of spacethat it takes to store the data. As seen in table 52′″, FIG. 41, thetotal number of bits is 283.

As seen in table 57′″. FIG. 42, the compression overhead in bits is 48.

Determining Whether the Compression Goal has been Achieved

Finally, we compare the original number of bits (384) to the currentnumber of bits (331) that are needed for this compression pass as seenin table 58′″, FIG. 43. In turn, we find that it takes 0.86 times asmany bits to store the compressed data as it took to store the originaldata.

Pass 5

In this pass, we replace the most highly occurring tuple from theprevious pass with a new symbol, and then we determine whether we haveachieved our compression goal.

Identifying all Possible Tuples

We expand the tuple array by adding the symbol that was created in theprevious pass. We add the symbol 5 as a first symbol and last symbol,and enter the tuples in the new cells as seen in table 35-4, FIG. 44.

Determining the Highly Occurring Tuple

The tuple array identifies the tuples that we look for and tally in ourrevised alphabet as seen in table 40-4, FIG. 45. (Total SymbolCount=136) The tuple that occurs most frequently is the symbol 2followed by symbol 5 (2>5), which has a hypotenuse of 5.4. It occurs 39times. This tuple ties with the tuple 0>2 (hypotenuse is 2) and 5>0(hypotenuse is 5). The tuple 2>5 is the most complex based on thehypotenuse length 25″ described above.

Creating a Symbol for the Highly Occurring Tuple

We define a new symbol 6 to represent the most highly occurring tuple2>5, and add it to the dictionary for the alphabet that was developed inthe previous passes as seen in table 26-5, FIG. 46.

Replacing the Tuple with the New Symbol

In the data stream, we replace every instance of the most highlyoccurring tuple with the new single symbol. We replace the 39 instancesof the 2>5 tuple in data stream 30-5, FIG. 39, with the symbol 6 as seenin data stream 30-6, FIG. 47.

Encoding the Alphabet

As demonstrated above, we count the number of symbols in the datastream, and use the count to build a Huffman tree and code for thecurrent alphabet as seen in table 41-5, FIG. 48. There is no Huffmancode assigned to the symbol 1 and the symbol 4 because there are noinstances of these symbols in the compressed data in this pass. Thetotal symbol count has been reduced from 136 to 97 (e.g., 40+1+8+9+39,but not including the EOF marker) as seen in table 52-4, FIG. 49.

Calculating the Compressed File Size

We need to evaluate whether our substitution reduces the amount of spacethat it takes to store the data. As seen in table 52-4, FIG. 49, thetotal number of bits is 187.

As seen in table 57-4, FIG. 50, the compression overhead in bits is 59.

Determining Whether the Compression Goal has been Achieved

Finally, we compare the original number of bits (384) to the currentnumber of bits (246, or 187+59) that are needed for this compressionpass as seen in table 58-4, FIG. 51. We find that it takes 0.64 times asmany bits to store the compressed data as it took to store the originaldata.

Pass 6

In this pass, we replace the most highly occurring tuple from theprevious pass with a new symbol, and then we determine whether we haveachieved our compression goal.

Identifying all Possible Tuples

We expand the tuple array 35-5 by adding the symbol that was created inthe previous pass as seen in FIG. 52. We add the symbol 6 as a firstsymbol and last symbol, and enter the tuples in the new cells.

Determining the Highly Occurring Tuple

The tuple array identifies the tuples that we look for and tally in ourrevised alphabet. (Total Symbol Count=97) The tuple that occurs mostfrequently is the symbol 0 followed by symbol 6 (0>6). It occurs 39times as seen in table 40-5, FIG. 53.

Creating a Symbol for the Highly Occurring Tuple

We define a new symbol 7 to represent the 0>6 tuple, and add it to thedictionary for the alphabet that was developed in the previous passes asseen in table 26-6, FIG. 54.

Replacing the Tuple with the New Symbol

In the data stream, we replace every instance of the most highlyoccurring tuple with the new single symbol. We replace the 39 instancesof the 0>6 tuple in data stream 30-6, FIG. 47, with the symbol 7 as seenin data stream 30-7, FIG. 55.

Encoding the Alphabet

As demonstrated above, we count the number of symbols in the datastream, and use the count to build a Huffman tree and code for thecurrent alphabet as seen in table 41-6, FIG. 56. There is no Huffmancode assigned to the symbol 1, symbol 4 and symbol 6 because there areno instances of these symbols in the compressed data in this pass. Thetotal symbol count has been reduced from 97 to 58 (e.g.,1+0+1+8+0+9+0+39, but not including the EOF marker).

Because all the symbols 1, 4, and 6 have been removed from the datastream, there is no reason to express them in the encoding scheme of theHuffman tree 50′. FIG. 57. However, the extinct symbols will be neededin the decode table. A complex symbol may decode to two less complexsymbols. For example, a symbol 7 decodes to 0>6.

We need to evaluate whether our substitution reduces the amount of spacethat it takes to store the data. As seen in table 52-5, FIG. 58, thetotal number of bits is 95.

As seen in table 57-5, FIG. 59, the compression overhead in bits is 71.

Determining Whether the Compression Goal has been Achieved

Finally, we compare the original number of bits (384) to the currentnumber of bits (166, or 95+71) that are needed for this compression passas seen in table 58-5, FIG. 60. We find that it takes 0.43 times as manybits to store the compressed data as it took to store the original data.

Subsequent Passes

Skilled artisans will also notice that overhead has been growing in sizewhile the total number of bits is still decreasing. We repeat theprocedure to determine if this is the optimum compressed file size. Wecompare the compression size for each subsequent pass to the firstoccurring lowest compressed file size. The chart 60, FIG. 61,demonstrates how the compressed file size grows, decreases, and thenbegins to grow as the encoding information and dictionary sizes grow. Wecan continue the compression of the foregoing techniques until the textfile compresses to a single symbol after 27 passes.

Interesting Symbol Statistics

With reference to table 61, FIG. 62, interesting statistics about thesymbols for this compression are observable. For instance, the top 8symbols represent 384 bits (e.g., 312+45+24+2+1) and 99.9% (e.g.,81.2+11.7+6.2+0.5+0.3%) of the file.

Storing the Compressed File

The information needed to decompress a file is usually written at thefront of a compressed file, as well as to a separate dictionary onlyfile. The compressed file contains information about the file, a codedrepresentation of the Huffman tree that was used to compress the data,the dictionary of symbols that was created during the compressionprocess, and the compressed data. The goal is to store the informationand data in as few bits as possible.

This section describes a method and procedure for storing information inthe compressed file.

File Type

The first four bits in the file are reserved for the version number ofthe file format, called the file type. This field allows flexibility forfuture versions of the software that might be used to write the encodeddata to the storage media. The file type indicates which version of thesoftware was used when we saved the file in order to allow the file tobe decompressed later.

Four bits allows for up to 16 versions of the software. That is, binarynumbers from 0000 to 1111 represent version numbers from 0 to 15.Currently, this field contains binary 0000.

Maximum Symbol Width

The second four bits in the file are reserved for the maximum symbolwidth. This is the number of bits that it takes to store in binary formthe largest symbol value. The actual value stored is four less than thenumber of bits required to store the largest symbol value in thecompressed data. When we read the value, we add four to the storednumber to get the actual maximum symbol width. This technique allowssymbol values up to 20 bits. In practical terms, the value 2^20 (2raised to the 20^(th) power) means that about 1 million symbols can beused for encoding.

For example, if symbols 0-2000 might appear in the compressed file, thelargest symbol ID (2000) would fit in a field containing 11 bits. Hence,a decimal 7 (binary 0111) would be stored in this field.

In the compression example, the maximum symbol width is the end-of-filesymbol 8, which takes four bits in binary (1000). We subtract four, andstore a value of 0000. When we decompress the data, we add four to zeroto find the maximum symbol width of four bits. The symbol width is usedto read the Huffman tree that immediately follows in the coded datastream.

Coded Huffman Tree

We must store the path information for each symbol that appears in theHuffman tree and its value. To do this, we convert the symbol's digitalvalue to binary. Each symbol will be stored in the same number of bits,as determined by the symbol with the largest digital value and stored asthe just read “symbol width”.

In the example, the largest symbol in the dictionary in the Huffmanencoded tree is the end-of-file symbol 8. The binary form of 8 is 1000,which takes 4 bits. We will store each of the symbol values in 4 bits.

To store a path, we will walk the Huffman tree in a method known as apre-fix order recursive parse, where we visit each node of the tree in aknown order. For each node in the tree one bit is stored. The value ofthe bit indicates if the node has children (1) or if it is a leaf withno children (0). If it is a leaf, we also store the symbol value. Westart at the root and follow the left branch down first. We visit eachnode only once. When we return to the root, we follow the right branchdown, and repeat the process for the right branch.

In the following example, the Huffman encoded tree is redrawn as 50-2 toillustrate the prefix-order parse, where nodes with children are labeledas 1, and leaf nodes are labeled as 0 as seen in FIG. 63.

The discovered paths and symbols are stored in the binary form in theorder in which they are discovered in this method of parsing. Write thefollowing bit string to the file, where the bits displayed inbold/underline represent the path, and the value of the 0 node aredisplayed without bold/underline. The spaces are added for readability;they are not written to media.

110 0101 110 0000 10 1000 0 0010 0 0011 0 0111

Encode Array for the Dictionary

The dictionary information is stored as sequential first/lastdefinitions, starting with the two symbols that define the symbol 2. Wecan observe the following characteristics of the dictionary:

-   -   The symbols 0 and 1 are the atomic (non-divisible) symbols        common to every compressed file, so they do not need to be        written to media.    -   Because we know the symbols in the dictionary are sequential        beginning with 2, we store only the symbol definition and not        the symbol itself.    -   A symbol is defined by the tuple it replaces. The left and right        symbols in the tuple are naturally symbols that precede the        symbol they define in the dictionary.    -   We can store the left/right symbols of the tuple in binary form.    -   We can predict the maximum number of bits that it takes to store        numbers in binary form. The number of bits used to store binary        numbers increases by one bit with each additional power of two        as seen, for example, in table 62, FIG. 64:

Because the symbol represents a tuple made up of lower-level symbols, wewill increase the bit width at the next higher symbol value; that is, at3, 5, 9, and 17, instead of at 2, 4, 8, and 16.

We use this information to minimize the amount of space needed to storethe dictionary. We store the binary values for the tuple in the order offirst and last, and use only the number of bits needed for the values.

Three dictionary instances have special meanings. The 0 and 1 symbolsrepresent the atomic symbols of data binary 0 binary 1, respectively.The last structure in the array represents the end-of-file (EOF) symbol,which does not have any component pieces. The EOF symbol is alwaysassigned a value that is one number higher than the last symbol found inthe data stream.

Continuing our compression example, the table 63, FIG. 65, shows how thedictionary is stored.

Write the following hit string to the file. The spaces are added forreadability; they are not written to media.

10 1000 0111 100000 010101 000110

Encoded Data

To store the encoded data, we replace the symbol with its matchingHuffman code and write the bits to the media. At the end of the encodedbit string, we write the EOF symbol. In our example, the finalcompressed symbol string is seen again as 30-7, FIG. 66, including theEOF.

The Huffman code for the optimal compression is shown in table 67, FIG.67.

As we step through the data stream, we replace the symbol with theHuffman coded bits as seen at string 68, FIG. 68. For example, wereplace symbol 0 with the bits 0100 from table 67, replace symbol 5 with00 from table 67, replace instances of symbol 7 with 1, and so on. Wewrite the following string to the media, and write the end of file codeat the end. The bits are separated by spaces for readability; the spacesare not written to media.

The compressed bit string for the data, without spaces is:

01000011111111111111111111111111101100111011001111111101100101100011000110001100011000101101010

Overview of the Stored File

As summarized in the diagram 69, FIG. 69, the information stored in thecompressed file is the file type, symbol width, Huffman tree,dictionary, encoded data, and EOF symbol. After the EOF symbol, avariable amount of pad bits are added to align the data with the finalbyte in storage.

In the example, the bits 70 of FIG. 70 are written to media. Spaces areshown between the major fields for readability; the spaces are notwritten to media. The “x” represents the pad bits. In FIG. 69, the bits70 are seen filled into diagram 69 b corresponding to the compressedfile format.

Decompressing the Compressed File

The process of decompression unpacks the data from the beginning of thefile 69, FIG. 69, to the end of the stream.

File Type

Read the first four bits of the file to determine the file formatversion.

Maximum Symbol Width

Read the next four bits in the file, and then add four to the value todetermine the maximum symbol width. This value is needed to read theHuffman tree information.

Huffman Tree

Reconstruct the Huffman tree. Each 1 bit represents a node with twochildren. Each 0 bit represents a leaf node, and it is immediatelyfollowed by the symbol value. Read the number of bits for the symbolusing the maximum symbol width.

In the example, the stored string for Huffman is:

11001011100000101000000100001100111

With reference to FIG. 71, diagram 71 illustrates how to unpack andconstruct the Huffman tree using the pre-fix order method.

Dictionary

To reconstruct the dictionary from file 69, read the values for thepairs of tuples and populate the table. The values of 0 and 1 are known,so they are automatically included. The bits are read in groups based onthe number of bits per symbol at that level as seen in table 72, FIG.72.

In our example, the following bits were stored in the file:

1010000111101000010101000110

We read the numbers in pairs, according to the bits per symbol, wherethe pairs represent the numbers that define symbols in the dictionary:

Bits Symbol 1 0 2 10 00 3 01 11 4 100 000 5 010 101 6 000 110 7

We convert each binary number to a decimal number:

Decimal Value Symbol 1 0 2 2 0 3 1 3 4 4 0 5 2 5 6 0 6 7

We identify the decimal values as the tuple definitions for the symbols:

Symbol Tuple 2 1 > 0 3 2 > 0 4 1 > 3 5 4 > 0 6 2 > 5 7 0 > 6

We populate the dictionary with these definitions as seen in table 73,FIG. 73.

Construct the Decode Tree

We use the tuples that are defined in the re-constructed dictionary tobuild the Huffman decode tree. Let's decode the example dictionary todemonstrate the process. The diagram 74 in FIG. 74 shows how we buildthe decode tree to determine the original bits represented by each ofthe symbols in the dictionary. The step-by-step reconstruction of theoriginal bits is as follows:

Start with symbols 0 and 1. These are the atomic elements, so there isno related tuple. The symbol 0 is a left branch from the root. Thesymbol 1 is a right branch. (Left and right are relative to the node asyou are facing the diagram—that is, on your left and on your right.) Theatomic elements are each represented by a single bit, so the binary pathand the original path are the same. Record the original bits 0 and 1 inthe decode table.

Symbol 2 is defined as the tuple 1>0 (symbol 1 followed by symbol 0). Inthe decode tree, go to the node for symbol 1, then add a path thatrepresents symbol 0. That is, add a left branch at node 1. Theterminating node is the symbol 2. Traverse the path from the root to theleaf to read the branch paths of left (L) and right (R). Replace eachleft branch with a 0 and each right path with a 1 to view the binaryforum of the path as LR, or binary 10.

Symbol 3 is defined as the tuple 2>0. In the decode tree, go to the nodefor symbol 2, then add a path that represents symbol 0. That is, add aleft branch at node 2. The terminating node is the symbol 3. Traversethe path from the root to the leaf to read the branch path of RLL.Replace each left branch with a 0 and each right path with a 1 to viewthe binary form of the path as 100.

Symbol 4 is defined as the tuple 1>3. In the decode tree, go to the nodefor symbol 1, then add a path that represents symbol 3. From the root tothe node for symbol 3, the path is RLL. At symbol 1, add the RLL path.The terminating node is symbol 4. Traverse the path from the root to theleaf to read the path of RRLL, which translates to the binary format of1100.

Symbol 5 is defined as the tuple 4>0. In the decode tree, go to the nodefor symbol 4, then add a path that represents symbol 0. At symbol 4, addthe L path. The terminating node is symbol 5. Traverse the path from theroot to the leaf to read the path of RRLLL, which translates to thebinary format of 11000.

Symbol 6 is defined as the tuple 2>5. In the decode tree, go to the nodefor symbol 2, then add a path that represents symbol 5. From the root tothe node for symbol 5, the path is RRLLL. The terminating node is symbol6. Traverse the path from the root to the leaf to read the path ofRLRRLLL, which translates to the binary format of 1011000.

Symbol 7 is defined as the tuple 0>6, In the decode tree, go to the nodefor symbol 0, then add a path that represents symbol 6. From the root tothe node for symbol 6, the path is RLRRLLL. The terminating node issymbol 7. Traverse the path from the root to the leaf to read the pathof LRLRRLLL, which translates to the binary format of 01011000.

Decompress the Data

To decompress the data, we need the reconstructed Huffman tree and thedecode table that maps the symbols to their original bits as seen at 75,FIG. 75. We read the bits in the data file one bit at a time, followingthe branching path in the Huffman tree from the root to a node thatrepresents a symbol.

The compressed file data bits are:

01000011111111111111111111111111101100111011001111111101100101100011000110001100011000101101010

For example, the first four bits of encoded data 0100 takes us to symbol0 in the Huffman tree, as illustrated in the diagram 76, FIG. 76. Welook up 0 in the decode tree and table to find the original bits. Inthis case, the original bits are also 0. We replace 0100 with the singlebit 0.

In the diagram 77 in FIG. 77, we follow the next two bits 00 to findsymbol 5 in the Huffman tree. We look up 5 in the decode tree and tableto find that symbol 5 represents original bits of 11000. We replace 00with 11000.

In the diagram 78, FIG. 78, we follow the next bit 1 to find symbol 7 inthe Huffman tree. We look up 7 in the decode tree and table to find thatsymbol 7 represents the original bits 01011000. We replace the singlebit 1 with 01011000. We repeat this for each 1 in the series of is thatfollow.

The next symbol we discover is with bits 011. We follow these bits inthe Huffman tree in diagram 79, FIG. 79. We look up symbol 3 in thedecode tree and table to find that it represents original bits 100, sowe replace 011 with bits 100.

We continue the decoding and replacement process to discover the symbol2 near the end of the stream with bits 01011, as illustrated in diagram80, FIG. 80. We look up symbol 2 in the decode tree and table to findthat it represents original bits 10, so we replace 01011 with bits 10.

The final unique sequence of bits that we discover is the end-of-filesequence of 01010, as illustrated in diagram 81, FIG. 81. The EOF tellsus that we are done unpacking.

Altogether, the unpacking of compressed bits recovers the original bitsof the original data stream in the order of diagram 82 spread across twoFIGS. 82 a and 82 b.

With reference to FIG. 83, a representative computing system environment100 includes a computing device 120. Representatively, the device is ageneral or special purpose computer, a phone, a PDA, a server, a laptop,etc., having a hardware platform 128. The hardware platform includesphysical I/O and platform devices, memory (M), processor (P), such as aCPU(s), USB or other interfaces (X), drivers (D), etc. In turn, thehardware platform hosts one or more virtual machines in the form ofdomains 130-1 (domain 0, or management domain), 130-2 (domain U1), . . .130-n (domain Un), each having its own guest operating system (O.S.)(e.g., Linux, Windows, Netware, Unix, etc.), applications 140-1, 140-2,. . . 140-n, file systems, etc. The workloads of each virtual machinealso consume data stored on one or more disks 121.

An intervening Xen or other hypervisor layer 150, also known as a“virtual machine monitor,” or virtualization manager, serves as avirtual interface to the hardware and virtualizes the hardware. It isalso the lowest and most privileged layer and performs schedulingcontrol between the virtual machines as they task the resources of thehardware platform, e.g., memory, processor, storage, network (N) (by wayof network interface cards, for example), etc. The hypervisor alsomanages conflicts, among other things, caused by operating system accessto privileged machine instructions. The hypervisor can also be type 1(native) or type 2 (hosted). According to various partitions, theoperating systems, applications, application data, boot data, or otherdata, executable instructions, etc., of the machines are virtuallystored on the resources of the hardware platform. Alternatively, thecomputing system environment is not a virtual environment at all, but amore traditional environment lacking a hypervisor, and partitionedvirtual domains. Also, the environment could include dedicated servicesor those hosted on other devices.

In any embodiment, the representative computing device 120 is arrangedto communicate 180 with one or more other computing devices or networks.In this regard, the devices may use wired, wireless or combinedconnections to other devices/networks and may be direct or indirectconnections. If direct, they typify connections within physical ornetwork proximity (e.g., intranet). If indirect, they typify connectionssuch as those found with the internet, satellites, radio transmissions,or the like. The connections may also be local area networks (LAN), widearea networks (WAN), metro area networks (MAN), etc., that are presentedby way of example and not limitation. The topology is also any of avariety, such as ring, star, bridged, cascaded, meshed, or other knownor hereinafter invented arrangement.

In still other embodiments, skilled artisans will appreciate thatenterprises can implement some or all of the foregoing with humans, suchas system administrators, computing devices, executable code, orcombinations thereof. In turn, methods and apparatus of the inventionfurther contemplate computer executable instructions, e.g., code orsoftware, as part of computer program products on readable media, e.g.,disks for insertion in a drive of a computing device 120, or availableas downloads or direct use from an upstream computing device. Whendescribed in the context of such computer program products, it isdenoted that items thereof, such as modules, routines, programs,objects, components, data structures, etc., perform particular tasks orimplement particular abstract data types within various structures ofthe computing system which cause a certain function or group offunction, and such are well known in the art.

While the foregoing produces a well-compressed output file, e.g., FIG.69, skilled artisans should appreciate that the algorithm requiresrelatively considerable processing time to determine a Huffman tree,e.g., element 50, and a dictionary, e.g., element 26, of optimal symbolsfor use in encoding and compressing an original file. Also, the timespent to determine the key information of the file is significantlylonger than the time spent to encode and compress the file with the key.The following embodiment, therefore, describes a technique to use afile's compression byproducts to compress other data files that containsubstantially similar patterns. The effectiveness of the resultantcompression depends on how similar a related file's patterns are to theoriginal file's patterns. As will be seen, using previously created, butrelated key, decreases the processing time to a small fraction of thetime needed for the full process above, but at the expense of a slightlyless effective compression. The process can be said to achieve a “fastapproximation” to optimal compression for the related files.

The definitions from FIG. 1 still apply.

Broadly, the “fast approximation” hereafter 1) greatly reduces theprocessing time needed to compress a file using the techniques above,and 2) creates and uses a decode tree to identify the most complexpossible pattern from an input bit stream that matches previouslydefined patterns. Similar to earlier embodiments, this encoding methodrequires repetitive computation that can be automated by computersoftware. The following discusses the logical processes involved.

Compression Procedure Using a Fast Approximation to Optimal Compression

Instead of using the iterative process of discovery of the optimal setof symbols, above, the following uses the symbols that were previouslycreated for another file that contains patterns significantly similar tothose of the file under consideration. In a high-level flow, the processinvolves the following tasks:

-   -   1. Select a file that was previously compressed using the        procedure(s) in FIGS. 2-82 b. The file should contain data        patterns that are significantly similar to the current file        under consideration for compression.    -   2. From the previously compressed file, read its key information        and unpack its

Huffman tree and symbol dictionary by using the procedure describedabove, e.g., FIGS. 63-82 b.

-   -   3. Create a decode tree for the current file by using the symbol        dictionary from the original file.    -   4. Identify and count the number of occurrences of patterns in        the current file that match the previously defined patterns.    -   5. Create a Huffman encoding tree for the symbols that occur in        the current file plus an end-of-file (EOF) symbol.    -   6. Store the information using the Huffman tree for the current        file plus the file type, symbol width, and dictionary from the        original file.        Each of the tasks is described in more detail below. An example        is provided thereafter.        Selecting a Previously Compressed File

The objective of the fast approximation method is to take advantage ofthe key information in an optimally compressed file that was created byusing the techniques above. In its uncompressed form of original data,the compressed file should contain data patterns that are significantlysimilar to the patterns in the current file under consideration forcompression. The effectiveness of the resultant compression depends onhow similar a related file's patterns are to the original file'spatterns. The way a skilled artisan recognizes a similar file is thatsimilar bit patterns are found in the originally compressed and new fileyet to be compressed. It can be theorized a priori that files are likelysimilar if they have similar formatting (e.g., text, audio, image,powerpoint, spreadsheet, etc), topic content, tools used to create thefiles, file type, etc. Conclusive evidence of similar bit patterns isthat similar compression ratios will occur on both files (i.e. originalfile compresses to 35% of original size, while target file alsocompresses to about 35% of original size). It should be noted thatsimilar file sizes are not a requisite for similar patterns beingpresent in both files.

With reference to FIG. 84, the key information 200 of a file includesthe file type, symbol width, Huffman tree, and dictionary from anearlier file, e.g., file 69, FIG. 69.

Reading and Unpacking the Key Information

From the key information 200, read and unpack the File Type, MaximumSymbol Width, Huffman Tree, and Dictionary fields.

Creating a Decode Tree for the Current File

Create a pattern decode tree using the symbol dictionary retrieved fromthe key information. Each symbol represents a bit pattern from theoriginal data stream. We determine what those bits are by building adecode tree, and then parsing the tree to read the bit patterns for eachsymbol.

We use the tuples that are defined in the re-constructed dictionary tobuild the decode tree. The pattern decode tree is formed as a tree thatbegins at the root and branches downward. A terminal node represents asymbol ID value. A transition node is a placeholder for a bit that leadsto terminal nodes.

Identifying and Counting Pattern Occurrences

Read the bit stream of the current file one bit at a time. As the datastream is parsed from left to right, the paths in the decode tree aretraversed to detect patterns in the data that match symbols in theoriginal dictionary.

Starting from the root of the pattern decode tree, use the value of eachinput bit to determine the descent path thru the pattern decode tree. A“0” indicates a path down and to the left, while a “1” indicates a pathdown and to the right. Continue descending through the decode tree untilthere is no more descent path available. This can occur because a branchleft is indicated with no left branch available, or a branch right isindicated with no right branch available.

When the end of the descent path is reached, one of the followingoccurs:

-   -   If the descent path ends in a terminal node, count the symbol ID        found there.    -   If the descent path ends in a transition node, retrace the        descent path toward the root, until a terminal node is        encountered. This terminal node represents the most complex        pattern that could be identified in the input bit stream. For        each level of the tree ascended, replace the bit that the path        represents back into the bit stream because those bits form the        beginning of the next pattern to be discovered. Count the symbol        ID found in the terminal node.

Return to the root of the decode tree and continue with the next bit inthe data stream to find the next symbol.

Repeat this process until all of the bits in the stream have beenmatched to patterns in the decode tree. When done, there exists a listof all of the symbols that occur in the bit stream and the frequency ofoccurrence for each symbol.

Creating a Huffman Tree and Code for the Current File

Use the frequency information to create a Huffman encoding tree for thesymbols that occur in the current file. Include the end-of-file (EOF)symbol when constructing the tree and determining the code.

Storing the Compressed File

Use the Huffman tree for the current file to encode its data. Theinformation needed to decompress the file is written at the front of thecompressed file, as well as to a separate dictionary only file. Thecompressed file contains:

The file type and maximum symbol width information from the originalfile's key

-   -   A coded representation of the Huffman tree that was created for        the current file and used to compress its data,    -   The dictionary of symbols from the original file's key.    -   The Huffman-encoded data, and    -   The Huffman-encoded EOF symbol.        Example of “Fast Approximation”

This example uses the key information 200 from a previously created butrelated compressed file to approximate the symbols needed to compress adifferent file.

Reading and Unpacking the Key Information

With reference to table 202, FIG. 85, a representative dictionary ofsymbols (0-8) was unpacked from the key information 200 for a previouslycompressed file. The symbols 0 and 1 are atomic, according to definition(FIG. 1) in that they represent bits 0 and 1, respectively. The readingand unpacking this dictionary from the key information is given above.

Construct the Decode Tree from the Dictionary

With reference to FIG. 86, a diagram 204 demonstrates the process ofbuilding the decode tree for each of the symbols in the dictionary (FIG.85) and determining the original bits represented by each of the symbolsin the dictionary. In the decode tree, there are also terminal nodes,e.g., 205, and transition nodes, e.g., 206. A terminal node represents asymbol value. A transition node does not represent a symbol, butrepresents additional bits in the path to the next symbol. Thestep-by-step reconstruction of the original bits is described below.

Start with symbols 0 and 1. These are the atomic elements, bydefinition, so there is no related tuple as in the dictionary of FIG.85. The symbol 0 branches left and down from the root. The symbol 1branches right and down from the root. (Left and right are relative tothe node as you are facing the diagram—that is, on your left and on yourright.) The atomic elements are each represented by a single bit, so thebinary path and the original path are the same. You record the “originalbits” 0 and 1 in the decode table 210, as well as its “branch path.”

Symbol 2 is defined from the dictionary as the tuple 1>0 (symbol 1followed by symbol 0). In the decode tree 212, go to the node for symbol1 (which is transition node 205 followed by a right path R and ending ina terminal node 206, or arrow 214), then add a path that representssymbol 0 (which is transition node 205 followed by a left path L andending in a terminal node 206, or path 216). That is, you add a leftbranch at node 1. The terminating node 220 is the symbol 2. Traverse thepath from the root to the leaf to read the branch paths of right (R) andleft (L). Replace each left branch with a 0 and each right path with a 1to view the binary form of the path as RL, or binary 10 as in decodetable 210.

Symbol 3 is defined as the tuple 2>0. In its decode tree 230, it is thesame as the decode tree for symbol 2, which is decode tree 212, followedby the “0.” Particularly, in tree 230, go to the node for symbol 2, thenadd a path that represents symbol 0. That is, you add a left branch(e.g., arrow 216) at node 2. The terminating node is the symbol 3.Traverse the path from the root to the leaf to read the branch path ofRLL. Replace each left branch with a 0 and each right path with a 1 toview the binary format of 100 as in the decode table.

Similarly, the other symbols are defined with decode trees building onthe decode trees for other symbols. In particular, they are as follows:

Symbol 4 from the dictionary is defined as the tuple 1>3. In its decodetree, go to the node for symbol 1, then add a path that representssymbol 3. From the root to the node for symbol 3, the path is RLL. Atsymbol 1, add the RLL path. The terminating node is symbol 4. Traversethe path from the root to the leaf to read the path of RRLL, whichtranslates to the binary format of 1100 as in the decode table.

Symbol 5 is defined as the tuple 4>0. In its decode tree, go to the nodefor symbol 4, then add a path that represents symbol 0. At symbol 4, addthe L path. The terminating node is symbol 5. Traverse the path from theroot to the leaf to read the path of RRLLL, which translates to thebinary format of 11000.

Symbol 6 is defined as the tuple 5>3. In its decode tree, go to the nodefor symbol 5, then add a path that represents symbol 3. The terminatingnode is symbol 6. Traverse the path from the root to the leaf to readthe path of RRLLLRLL, which translates to the binary format of 11000100.

Symbol 7 is defined from the dictionary as the tuple 5>0. In its decodetree, go to the node for symbol 5, then add a path that representssymbol 0. From the root to the node for symbol 5, the path is RRLLL. Adda left branch. The terminating node is symbol 7. Traverse the path fromthe root to the leaf to read the path of RRLLLL, which translates to thebinary format of 110000.

Finally, symbol 8 is defined in the dictionary as the tuple 7>2. In itsdecode tree, go to the node for symbol 7, then add a path thatrepresents symbol 2. From the root to the node for symbol 7, the path isRRLLLL. Add a RL path for symbol 2. The terminating node is symbol 8.Traverse the path from the root to the leaf to read the path ofRRLLLLRL, which translates to the binary format of 11000010.

The final decode tree for all symbols put together in a single tree iselement 240, FIG. 87, and the decode table 210 is populated with alloriginal bit and branch path information.

Identifying and Counting Pattern Occurrences

For this example, the sample or “current file” to be compressed issimilar to the one earlier compressed who's key information 200. FIG.84, was earlier extracted. It contains the following representative “bitstream” (reproduced in FIG. 88, with spaces for readability):0110000101100010011000010110001001100001011000010110001001100001011000100110000101100001011000100110000101100010011000010110001001100001011000100110001001100010011000100110001001100001011000010110001001100001011000100110000101100010

We step through the stream one bit at a time to match patterns in thestream to the known symbols from the dictionary 200, FIG. 85. Todetermine the next pattern in the bit stream, we look for the longestsequence of bits that match a known symbol. To discover symbols in thenew data bit stream, read a single bit at a time from the input bitstream. Representatively, the very first bit, 250 FIG. 88, of the bitstream is a “0.” With reference to the Decode Tree, 240 in FIG. 87,start at the top-most (the root) node of the tree. The “0” input bitindicates a down and left “Branch Path” from the root node. The next bitfrom the source bit stream at position 251 in FIG. 88, is a “1,”indicating a down and right path. The Decode Tree does not have adefined path down and right from the current node. However the currentnode is a terminal node, with a symbol ID of 0. Write a symbol 0 to atemporary file, and increment the counter corresponding to symbol ID 0.Return to the root node of the Decode Tree, and begin looking for thenext symbol. The “1” bit that was not previously usable in the decode(e.g., 251 in FIG. 88) indicates a down and right. The next bit “1” (252in FIG. 88) indicates a down and right. Similarly, subsequent bits“000010” indicate further descents in the decode tree with pathsdirections of LLLLRL, resulting in path 254 from the root. The next bit“1” (position 255, FIG. 88) denotes a further down and right path, whichdoes not exist in the decode tree 240, as we are presently at a terminalnode. The symbol ID for this terminal node is 8. Write a symbol 8 to thetemporary file, and increment the counter corresponding to symbol ID 8.

Return to the root node of the Decode Tree, and begin looking for thenext symbol again starting with the last unused input stream bit, thebit “1” at position 255, FIG. 88. Subsequent bits in the source bitstream. “11000100,” lead down through the Decode Tree to a terminal nodefor symbol 6. The next bit, “1”, at position 261, FIG. 88, does notrepresent a possible down and right traversal path. Thus, write a symbol6 to the temporary file, and increment the counter corresponding tosymbol ID 6. Again, starting back at the root of the tree, performsimilar decodes and book keeping to denote discovery of symbols86886868868686866666886868. Starting again at the root of the DecodeTree, parse the paths represented by input bits “1100010” beginning atposition 262. There are no more bits available in the input stream.However, the current position in the Decode Tree, position 268, does notidentify a known symbol. Thus, retrace the Decode Tree path upwardtoward the root. On each upward level node transition, replace a bit atthe front of the input bit stream with a bit that represents that pathtransition; e.g. up and right is a “0” up and left is a “1”. Continuethe upward parse until reaching a valid symbol ID node, in this case thenode 267 for symbol ID 5. In the process, two bits (e.g., positions 263and 264, FIG. 88) will have been pushed back onto the input stream, a“0”, and then a “1.” As before, write a symbol 5 to a temporary file,and increment the counter corresponding to symbol ID 5. Starting back atthe root of the tree, bits are pulled from the input stream and parseddownward, in this case the “1” and then the “0” at positions 263 and264. As we are now out of input bits, after position 264, examine thecurrent node for a valid symbol ID, which in this case does exist atnode 269, a symbol ID of 2. Write a symbol 2 to the temporary files,increment the corresponding counter. All input bits have now beendecoded to previously defined symbols. The entire contents of thetemporary file are symbols: “0868688686886868686666688686852.”

From here, the frequency of occurrence of each of the symbols in the newbit stream is counted. For example, the symbols “0” and 2″ are eachfound occurring once at the beginning and end of the new bit stream.Similarly, the symbol “5” is counted once just before the symbol “2.”Each of the symbols “6” and “8” are counted fourteen times in the middleof the new bit stream for a total of thirty-one symbols. Its result isshown in table 275, FIG. 89. Also, one count for the end of file (EOF)symbol is added that is needed to mark the end of the encoded data whenwe store the compressed data.

Creating a Huffman Tree and Code for the Current File

From the symbol “counts” in FIG. 89, a Huffman binary code tree 280 isbuilt for the current file, as seen in FIG. 90. There is no Huffman codeassigned to the symbol 1, symbol 3, symbol 4, and symbol 7 because thereare no instances of these symbols in the new bit stream. However, theextinct symbols will be needed in the decode table for the tree. Thereason for this is that a complex symbol may decode to two less complexsymbols. For example, it is known that a symbol 8 decodes to tuple 7>2,e.g., FIG. 85.

To construct the tree 280, list first the symbols from highest count tolowest count. In this example, the symbol “8” and symbol “6” tied with acount of fourteen and are each listed highest on the tree. On the otherhand, the least counted symbols were each of symbol “0,” “2,” “5,” andthe EOF. Combine the counts for the two least frequently occurringsymbols in the dictionary. This creates a node that has the value of thesum of the two counts. In this example, the EOF and 0 are combined intoa single node 281 as are the symbols 2 and 5 at node 283. Together, allfour of these symbols combine into a node 285. Continue combining thetwo lowest counts in this manner until there is only one symbolremaining. This generates a Huffman binary code tree.

Label the code tree paths with zeros (0s) and ones (1s). To encode asymbol, parse from the root to the symbol. Each left and down pathrepresents a 0 in the Huffman code. Each right and down path representsa 1 in the Huffman code. The Huffman coding scheme assigns shorter codewords to the more frequent symbols, which helps reduce the size lengthof the encoded data. The Huffman code for a symbol is defined as thestring of values associated with each path transition from the root tothe symbol terminal node.

With reference to FIG. 91, table 290 shows the final Huffman code forthe current file, as based on the tree. For example, the symbol “8”appears with the Huffman code 0. From the tree, and knowing the rulethat “0” is a left and down path, the “8” should appear from the root atdown and left, as it does. Similarly, the symbol “5” should appear at“1011” or right and down, left and down, right and down, and right anddown, as it does. Similarly, the other symbols are found. There is nocode for symbols 1, 3, 4, and 7, however, because they do not appear inthe current file.

Storing the Compressed File

The diagram in FIG. 92 illustrates how we now replace the symbols withtheir Huffman code value when the file is stored, such as in file formatelement 69, FIG. 69. As is seen, the diagram 295 shows the original bitstream that is coded to symbols or a new bit stream, then coded toHuffman codes. For example, the “0” bit at position 250 in the originalbit stream coded to a symbol “0” as described in FIG. 88. By replacingthe symbol 0 with its Huffman code (1001) from table 290, FIG. 91, theHuffman encoded bits are seen, as:

1001 0 11 0 110 0 11 0 11 0 0 11 0 11 0 11 0 11 11 11 11 11 0 0 11 0 110 1011 1010 1000

Spaces are shown between the coded bits for readability; the spaces arenot written to media. Also, the code for the EOF symbol (1000) is placedat the end of the encoded data and shown in underline.

With reference to FIG. 93, the foregoing information is stored in thecompressed file 69′ for the current file. As skilled artisans willnotice, it includes both original or re-used information and newinformation, thereby resulting in a “fast approximation.” In detail, itincludes the file type from the original key information (200), thesymbol width from the original key information (200), the new Huffmancoding recently created for the new file, the dictionary from the keyinformation (200) of the original file, the data that is encoded byusing the new Huffman tree, and the new EOF symbol. After the EOFsymbol, a variable amount of pad bits are added to align the data withthe final byte in storage.

In still another alternate embodiment, the following describestechnology to identify a file by its contents. It is defined, in onesense, as providing a file's “digital spectrum.” The spectrum, in turn,is used to define a file's position in an N-dimensional universe. Thisuniverse provides a basis by which a file's position determinessimilarity, adjacency, differentiation and grouping relative to otherfiles. Ultimately, similar files can originate many new compressionfeatures, such as the “fast approximations” described above. Theterminology defined in FIG. 1 remains valid as does theearlier-presented information for compression and/or fast approximationsusing similar files. It is supplemented with the definitions in FIG. 94.Also, the following considers an alternate use of the earlier describedsymbols to define a digital variance in a file. For simplicity in thisembodiment, a data stream under consideration is sometimes referred toas a “file.”

The set of values that digitally identifies the file, referred to as thefile's digital spectrum, consists of several pieces of information foundin two scalar values and two vectors.

The scalar values are:

-   -   The number of symbols in the symbol dictionary (the dictionary        being previously determined above.)    -   The number of symbols also represents the number of dimensions        in the N-dimensional universe, and thus, the number of        coordinates in the vectors.    -   The length of the source file in bits.    -   This is the total number of bits in the symbolized data stream        after replacing each symbol with the original bits that the        symbol represents.        The vectors are:    -   An ordered vector of frequency counts, where each count        represents the number of times a particular symbol is detected        in the symbolized data stream.        F _(x)=(F _(0x) ,F _(1x) ,F _(2x) ,F _(3x) , . . . ,F _(Nx)),    -   where F represents the symbol frequency vector, 0 to N are the        symbols in a file's symbol dictionary, and x represents the        source file of interest.    -   An ordered vector of hit lengths, where each bit length        represents the number of bits that are represented by a        particular symbol.        B _(x)=(B _(0x) ,B _(1x) ,B _(2x) ,B _(3x) , . . . ,B _(Nx)),    -   where B represents the bit-length vector, 0 to N are the symbols        in a file's symbol dictionary, and x represents the source file        of interest.

The symbol frequency vector can be thought of as a series of coordinatesin an N-dimensional universe where N is the number of symbols defined inthe alphabet of the dictionary, and the counts represent the distancefrom the origin along the related coordinate axis. The vector describesthe file's informational position in the N-dimension universe. Themeaning of each dimension is defined by the meaning of its respectivesymbol.

The origin of N-dimensional space is an ordered vector with a value of 0for each coordinate:F _(O)=(0,0,0,0,0,0,0,0, . . . ,0).

The magnitude of the frequency vector is calculated relative to theorigin. An azimuth in each dimension can also be determined usingordinary trigonometry, which may be used at a later time. By usingPythagorean geometry, the distance from the origin to any point F_(x) inthe N-dimensional space can be calculated, i.e.:D _(ox)=square root(((F _(0x) −F _(0o))^2)+((F _(1x) −F _(1o))^2)+((F_(2x) −F _(2o))^2)+((F _(3x) −F _(3o)))^2)+ . . . +((F _(Nx) −F_(No))^2))

Substituting the 0 at each coordinate for the values at the origin, thesimplified equation is:D _(ox)=square root((F _(0x))^2)+(F _(1x))^2)+(F _(2x))^2)+(F _(3x))^2)+. . . +(F _(Nx))^2))

As an example, imagine that a file has 10 possible symbols and thefrequency vector for the file is:F _(x)=(3,5,6,1,0,7,19,3,6,22).

Since this vector also describes the file's informational position inthis 10-dimension universe, its distance from the origin can becalculated using the geometry outlined. Namely:Dox=squareroot(((3−0)^2)+((5−0)^2)+((6−0)^2)+((6−0)^2)+((1−0)^2)+((0−0)^2)+((7−0)^2)+((19−0)^2)+((3−0)^2)+((6−0)^2)+((22−0)^2))Dox=31.78.Determining a Characteristic Digital Spectrum

To create a digital spectrum for a file under current consideration, webegin with the key information 200, FIG. 84, which resulted from anoriginal file of interest. The digital spectrum determined for thisoriginal file is referred to as the characteristic digital spectrum. Adigital spectrum for a related file of interest, on the other hand, isdetermined by its key information from another file. Its digitalspectrum is referred to as a related digital spectrum.

The key information actually selected for the characteristic digitalspectrum is considered to be a “well-suited key.” A “well-suited key” isa key best derived from original data that is substantially similar tothe current data in a current file or source file to be examined. Thekey might even be the actual compression key for the source file underconsideration. However, to eventually use the digital spectruminformation for the purpose of file comparisons and grouping, it isnecessary to use a key that is not optimal for any specific file, butthat can be used to define the N-dimensional symbol universe in whichall the files of interest are positioned and compared. The more closelya key matches a majority of the files to be examined, the moremeaningful it is during subsequent comparisons.

The well-suited key can be used to derive the digital spectruminformation for the characteristic file that we use to define theN-dimensional universe in which we will analyze the digital spectra ofother files. From above, the following information is known about thecharacteristic digital spectrum of the file:

-   -   The number of symbols (N) in the symbol dictionary    -   The length of the source file in bits    -   An ordered vector of symbol frequency counts        F _(i)=(F _(0i) ,F _(1i) ,F _(2i) ,F _(3i) , . . . ,F _(Ni)),    -   where F represents the symbol frequency, 0 to N are the symbols        in the characteristic file's symbol dictionary, and i represents        the characteristic file of interest.    -   An ordered vector of bit lengths        B _(i)=(B _(0i) ,B _(1i) ,B _(3i) , . . . ,B _(Ni)),    -   where B represents the bit-length vector, 0 to N are the symbols        in the characteristic file's symbol dictionary, and i represents        the characteristic file of interest.        Determining a Related Digital Spectrum

Using the key information and digital spectrum of the characteristicfile, execute the process described in the fast approximation embodimentfor a current, related file of interest, but with the following changes:

-   -   1. Create a symbol frequency vector that contains one coordinate        position for the set of symbols described in the characteristic        file's symbol dictionary.        F _(j)=(F _(0j) ,F _(1j) ,F _(2j) ,F _(3j) , . . . ,F _(Nj)),        -   where F represents the symbol frequency, 0 to N are the            symbols in the characteristic file's symbol dictionary, and            j represents the related file of interest. Initially, the            count for each symbol is zero (0).    -   2. Parse the data stream of the related file of interest for        symbols. As the file is parsed, conduct the following:        -   a. Tally the instance of each discovered symbol in its            corresponding coordinate position in the symbol frequency            vector. That is, increment the respective counter for a            symbol each time it is detected in the source file.        -   b. Do not Huffman encode or write the detected symbol.        -   c. Continue parsing until the end of the file is reached.    -   3. At the completion of the source file parsing, write a digital        spectrum output file that contains the following:        -   a. The number of symbols (N) in the symbol dictionary        -   b. The length of the source file in bits        -   c. The symbol frequency vector developed in the previous            steps.            F _(j)=(F _(0v) ,F _(1j) ,F _(2j) ,F _(3j) , . . . F _(Nj)),            -   where F represents the frequency vector, 0 to N are the                symbols in the characteristic file's symbol dictionary,                and the j represents the file of interest.        -   d. The bit length vector            B _(j)=(B _(0j) ,B _(1j) ,B _(2j) ,B _(3j) , . . . ,B            _(Nj)),            -   where B represents the bit-length vector, 0 to N are the                symbols in the characteristic file's symbol dictionary,                and j represents the file of interest.                Advantages of Digital Spectrum Analysis

The digital spectrum of a file can be used to catalog a file's positionin an N-dimensional space. This position in space, or digital spectrum,can be used to compute “distances” between file positions, and hencesimilarity, e.g., the closer the distance, the closer the similarity.The notion of a digital spectrum may eventually lead to the notion of aself-cataloging capability of digital files, or other.

Begin: Example Defining a File's Digital Spectrum

To demonstrate the foregoing embodiment, the digital spectrum will bedetermined for a small data file that contains the following simpleASCII characters:aaaaaaaaaaaaaaaaaaaaaaaaaaabaaabaaaaaaaababbbbbb  (eqn. 100)

Each character is stored as a sequence of eight bits that correlates tothe ASCII code assigned to the character. The bit values for eachcharacter are:a=01100001  (eqn. 101)b=01100010  (eqn. 102)

By substituting the bits of equations 101 and 102 for the “a” and “b”characters in equation 100, a data stream 30 results as seen in FIG. 9.(Again, the characters are separated in the Figure with spaces forreadability, but the spaces are not considered, just the characters.)

After performing an optimal compression of the data by using the processdefined above in early embodiments, the symbols remaining in the datastream 30-7 are seen in FIG. 55. Alternatively, they are shown here as:0 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3 5 7 7 7 3 57 7 7 7 7 7 7 7 3 5 7 3 5 3 5 3 5 3 5 3 5 2  (eqn. 103)

With reference to FIG. 95, table 300 identifies the symbol definitionsfrom equation 103 and the bits they represent. The symbol definition 302identifies the alphabet of symbols determined from the data during thecompression process. The symbols 0 and 1 are atomic symbols andrepresent original bits 0 and 1, by definition. The subsequent symbols,i.e., 2-7, are defined by tuples, or ordered pairs of symbols, that arerepresented in the data, e.g., symbol 4 corresponds to a “1” followed bya “3,” or 1>3. In turn, each symbol represents a series or sequence ofbits 304 in the data stream of equation 103 (the source file), e.g.,symbol 4 corresponds to original bits 1100.

With reference to table 310, FIG. 96, the number of occurrences of eachsymbol is counted in the data stream (equation 103) and the number ofbits represented by each symbol is counted. For example, the symbol “7”in equation 103 appears thirty nine (39) times. In that its originalbits 304, correspond to “01011000.” it has eight (8) original bitsappearing in the data stream for every instance of a “symbol 7”appearing. For a grand total of numbers of bits, the symbol count 312 ismultiplied by the bit length 314 to arrive at a bit count 316. In thisinstance, thirty nine (39) is multiplied by eight (8) to achieve a bitcount of three-hundred twelve (312) for the symbol 7. A grand total ofthe number of bit counts 316 for every symbol 320 gives a length of thesource file 325 in numbers of bits. In this instance, the source filelength (in bits) is three-hundred eighty-four (384).

In turn, the scalar values to be used in the file's digital spectrumare:

-   -   Source File Length in bits=384    -   Number of Symbols=8 total (or symbols 0 through 7, column 320,        FIG. 96) The vectors to be used in the file's digital spectrum        are:    -   Frequency spectrum, F_(x), represented by the ordered vector of        counts for each symbol, from column 312, FIG. 96:        F _(x)=(1,0,1,8,0,9,0,39)    -   Bit length spectrum, Bx, is represented by the ordered vector of        counts for the original bits in the file that are represented by        each symbol, from column 314, FIG. 96:        B _(x)=(1,1,2,3,4,5,7,8)

The digital spectrum information can be used to calculate various usefulcharacteristics regarding the file from which it was derived, as well asits relationship to other spectra, and the files from which the otherspectra were derived. As an example, the frequency spectrum F(x) shownabove, may be thought to describe a file's informational position in an8-dimension universe, where the meaning of each dimension is defined bythe meaning of its respective symbols.

Since the origin of the 8-dimensional space is an ordered vector with avalue of 0 at each symbol position, e.g., F(0) (0,0,0,0,0,0,0,0), theinformational position in 8-dimensional space can be defined as anazimuth and distance from the origin. The magnitude of the positionvector is calculated using Pythagorean geometry. Dist(x,0)=sqrt(((F(x,0)−F(00)^2)+ . . . (F(x,7)−F(0,7)^2)). Simplified, this magnitudebecomes Dist(x,0)=sqrt((F(x,0)^2+F(x,2)^2+F(x,3)^2 . . . F(x,7)^2)).Using the values above in F_(x), the magnitude of the Dist(x,0)=40.84,or D_(x0)=square root(((1)^2)+((0)^2)+((1)^2)+((8)^2)+((0)^2)+((9)^2)+((0)^2)+((39)^2))=squareroot (1+0+1+64+0+81+0+1521)=40.84. Azimuth of the vector can be computedusing basic trigonometry.

Using information found in the digital spectra of a group of files, ananalysis can be done to determine similarity, or not, of two or moresubject files. Information from the digital spectrum is used to createan information statistic for a file. Statistics found to be pertinent indoing this analysis include at least:

S1) Frequency of occurrence of each possible symbol (FREQ)

S2) Normalized frequency of occurrence of each possible symbol (NORMFREQ)

S3) Informational content of occurrence of each symbol (INFO)

S4) Normalized information content of occurrence of each symbol (NORMINFO)

For ease of reference, statistic S1 can be called FREQ for frequency,statistic S2 can be called NORM FREQ for normalized frequency, statisticS1 can be called INFO for informational content, and statistic S4 can becalled NORM INFO for normalized informational content. A furtherdiscussion is given below for each of these statistical values.

As a first example, a digital spectra of three files, F1, F2, and F3 isgiven with respect to a common set of “N” symbols, e.g., symbols 1,symbol 2 and symbol 3. Each file is processed looking for the number oftimes each symbol is found in the file. The frequency of each symbol asit is found in each file is recorded along with a total number ofsymbols in each file. For this example, their respective spectra are:

File Description Total Symbol 1 Symbol 2 Symbol 3 File 1 Number ofSymbols 3 Sum of all Symbol 9 Occurrences Symbol frequencies 2 4 3Symbol bits sized 7 6 10 File 2 Number of Symbols 3 Sum of all Symbol 8Occurrences Symbol frequencies 4 2 2 Symbol bits sized 7 6 10 File 3Number of Symbols 3 Sum of all Symbol 27 Occurrences Symbol frequencies8 11 8 Symbol bits sized 7 6 10

Using a relevant pattern-derived statistic (possibly including S1, S2,S3, or S4 above), a vector of values is calculated for the N symboldefinitions that may occur in each file. A position in N-dimensionalspace is determined using this vector, where the distance along eachaxis in N-space is determined by the statistic describing itscorresponding symbol.

Specifically in this example, we will use statistic S1 (FREQ) and wehave three (3) common symbols that we are using to compare these filesand so a 3-dimensional space is determined. Each file is then defined asa position in this 3-dimensional space using a vector of magnitude 3 foreach file. The first value in each vector is the frequency of symbol 1in that file, the second value is the frequency of symbol 2, and thethird value is the frequency of symbol 3.

With reference to FIG. 97, these three example files are plotted. Thefrequency vectors are F1=(2, 4, 3), F2=(4, 2, 2), and F3=(8, 11, 8). Therelative position in 3-space (N=3) for each of these files is readilyseen.

A matrix is created with the statistic chosen to represent each file. Amatrix using the symbol frequency as the statistic looks like thefollowing:

FileID Sym1 Sym2 Sym3 F1 2 4 3 F2 4 2 2 F3 8 11 8

Using Pythagorean arithmetic, the distance (D) between the positions ofany two files (Fx, Fy) is calculated as

$\begin{matrix}{{D\left( {{Fx},{Fy}} \right)} = \sqrt{\left( {{Fx}_{1} - {Fy}_{1}} \right)^{2} + \left( {{Fx}_{2} - {Fy}_{2}} \right)^{2} + \left( {{Fx}_{n} - {Fy}_{n}} \right)^{2}}} & (1)\end{matrix}$In the example above, the distance between the position of F1 and F2 is

$\begin{matrix}{\sqrt{\left( {2 - 4} \right)^{2} + \left( {4 - 2} \right)^{2} + \left( {3 - 2} \right)^{2}} = {\sqrt{\left( {4 + 4 + 1} \right)} = {\sqrt{9} = 3.00}}} & (2)\end{matrix}$Similarly, the distance between F1 and F3 is found by

$\begin{matrix}{\sqrt{\left( {2 - 8} \right)^{2} + \left( {4 - 11} \right)^{2} + \left( {3 - 8} \right)^{2}} = {{\sqrt{\left( {36 + 49 + 25} \right)} + \sqrt{110}} = 10.49}} & (3)\end{matrix}$

A matrix of distances between all possible files is built. In the aboveexample this matrix would look like this:

Distance between files F1 F2 F3 F1 0.00 3.00 10.49 F2 3.00 0.00 11.53 F310.49 11.53 0.00

It can be seen graphically in FIG. 97, that the position of File 1 iscloser to File 2 than it is to File 3. It can also be seen in FIG. 97that File 2 is closer to File 1 than it is to File 3. File 3 is closestto File 1; File 2 is slightly further away.

Each row of the matrix is then sorted, such that the lowest distancevalue is on the left, and the highest value is on the right. During thesort process, care is taken to keep the File ID associated with eachvalue. The intent is to determine an ordered distance list with eachfile as a reference. The above matrix would sort to this:

Sorted Distance between files File Distance F1 F1 (0.00) F2 (3.00) F3(10.49) F2 F2 (0.00) F1 (3.00) F3 (11.53) F3 F3 (0.00)  F1 (10.49) F2(11.53)

Using this sorted matrix, the same conclusions that were previouslyreached by visual examination can now be determined mathematically.Exclude column 1, wherein it is obvious that the closest file to a givenfile is itself (or a distance value of 0.00). Column 2 now shows thatthe closest neighbor to F1 is F2, the closest neighbor to F2 is F1, andthe closest neighbor the F3 is F1.

Of course, this concept can be expanded to hundreds, thousands, ormillions or more of files and hundreds, thousands, or millions or moreof symbols. While the matrices and vectors are larger and might takemore time to process, the math and basic algorithms are the same. Forexample, consider a situation in which there exist 10,000 files and2,000 symbols.

Each file would have a vector of length 2000. The statistic chosen torepresent the value of each symbol definition with respect to each fileis calculated and placed in the vector representing that file. Aninformation position in 2000-space (N=2000) is determined by using thevalue in each vector position to represent the penetration along theaxis of each of the 2000 dimensions. This procedure is done for eachfile in the analysis. With the statistic value matrix created, thedistances between each file position are calculated using the abovedistance formula. A matrix that has 10,000 by 10,000 cells is created,for the 10,000 files under examination. The content of each cell is thecalculated distance between the two files identified by the row andcolumn of the matrix. The initial distance matrix would be 10,000×10,000with the diagonal values all being 0. The sorted matrix would also be10,000 by 10,000 with the first column being all zeros.

In a smaller example, say ten files, the foregoing can be much moreeasily demonstrated using actual tables represented as text tables inthis document. An initial matrix containing the distance information often files might look like this.

Distance Matrix Files F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F1 0.0 17.4 3.586.4 6.7 99.4 27.6 8.9 55.1 19.3 F2 17.4 0.0 8.6 19.0 45.6 83.2 19.9 4.549.2 97.3 F3 3.5 8.6 0.0 33.7 83.6 88.6 42.6 19.6 38.2 89.0 F4 86.4 19.033.7 0.0 36.1 33.6 83.9 36.2 48.1 55.8 F5 6.7 45.6 83.6 36.1 0.0 38.036.9 89.3 83.4 28.9 F6 99.4 83.2 88.6 33.6 38.0 0.0 38.4 11.7 18.4 22.0F7 27.6 19.9 42.6 83.9 36.9 38.4 0.0 22.6 63.3 35.7 F8 8.9 4.5 19.6 36.289.3 11.7 22.6 0.0 8.1 15.3 F9 55.1 49.2 38.2 48.1 83.4 18.4 63.3 8.10.0 60.2 F10 19.3 97.3 89.0 55.8 28.9 22.0 35.7 15.3 60.2 0.0

The distances in each row are then sorted such that an ordered list ofdistances, relative to each file, is obtained. The file identityrelation associated with each distance is preserved during the sort. Theresulting matrix now looks like this:

Sorted Distance Matrix 1 2 3 4 5 6 7 8 9 10 F1 F1 (0.0) F3 (3.5) F5(6.7) F8 (8.9) F2 (17.4) F10 (19.3) F7 (27.6) F9 (55.1) F4 (86.4) F6(99.4) F2 F2 (0.0) F8 (4.5) F3 (8.6) F1 (17.4) F4 (19.0) F7 (19.9) F5(45.6) F9 (49.2) F6 (83.2) F10 (97.3) F3 F3 (0.0) F1 (3.5) F2 (8.6) F8(19.6) F4 (33.7) F9 (38.2) F7 (42.6) F5 (83.6) F6 (88.6) F10 (89.0) F4F4 (0.0) F2 (19.0) F6 (33.6) F3 (33.7) F5 (36.1) F8 (36.2) F9 (48.1) F10(55.8) F1 (86.4) F7 (83.9) F5 F5 (0.0) F1 (6.7) F10 (28.9) F4 (36.1 F7(36.9) F6 (38.0) F2 (45.6) F9 (83.4) F3 (83.6) F8 (89.3) F6 F6 (0.0) F8(11.7) F9 (18.4) F10 (22.0) F4 (33.6) F5 (38.0) F7 (38.4 F2 (83.2) F3(88.6 F1 (99.4) F7 F7 (0.0) F2 (19.9) F8 (22.6) F1 (27.6) F5 (36.9) F10(35.7) F6 (38.4) F3 (42.6) F9 (63.3 F4 (83.9) F8 F8 (0.0) F2 (4.5) F9(8.1) F1 (8.9) F6 (11.7) F10 (15.3 F3 (19.6 F7 (22.6) F4 (36.2) F5(89.3) F9 F9 (0.0 F8 (8.1) F6 (18.4) F3 (38.2) F4 (48.1) F2 (49.2) F1(55.1) F10 (60.2) F7 (63.3) F5 (83.4) F10 F10 (0.0 F8 (15.3 F1 (19.3) F6(22.0) F5 (28.9) F7 (35.7) F4 (55.8) F9 (60.2) F3 (89.0) F2 (97.3)

Using the information in columns 1 and 2 a relationship graph can becreated of closest neighbor files. From the above matrix, skilledartisans will note the following:

F1's nearest neighbor is F3. Create a group. G1, assign these two filesto that group.

F2's nearest neighbor is F8. Create a group. G2, assign these two filesto that group.

F3 has already been assigned, its nearest neighbor is F1, and theybelong to group G1.

F4's nearest neighbor is F2, which already belongs to G2. Assign F4 toG2 as well.

F5's nearest neighbor is F1, which already belongs to G1. Assign F5 toG1 as well.

F6's nearest neighbor is F8 which already belongs to G2. Assign F6 to G2as well.

F7's nearest neighbor is F2, which already belongs to G2. Assign F7 toG2 also.

F8's has already been assigned. It's nearest neighbor is F2, and theybelong to G2.

F9's nearest neighbor is F8, which already belongs to G2. Assign F9 toG2 also.

F10's nearest neighbor is F8, which already belongs to G2. Assign F10 toG2 also.

The above “nearest neighbor” logic leads to the conclusion that twogroups (G1 and G2) of files exist. Group G1 contains F1, F3, F5, whileGroup G2 contains F2, F4, F6, F7, F8, F9, and F10.

An algorithm for determining groups based on adjacent neighbors is givenin FIG. 98A. For each file in the scope of analysis 900, a closestneighbor is determined, 910. From the example, this includes using thedistance values that have been sorted in columns 1 and 2. If a closestneighbor already belongs to a group at 920, the file joins that group at930. Else, if the closest neighbor belongs to no group at 940, a newgroup is created at 950 and both files are added to the new group at960. From the example. F1's nearest neighbor is F3 and no groups existat 940. Thus, a new group G1 is created at 950 and both F1 and F3 areassigned, or added. Similarly, F2's nearest neighbor is F8, but onlygroup G1 exists. Thus, a new group G2 is created at 950 for files F2 andF8 at 960. Later, it is learned that F4's nearest neighbor is F2, whichalready belongs to G2 at step 920. Thus, at 930 file F4 joins group G2.Once all files have been analyzed, the groups are finalized and groupprocessing ceases at 970.

With reference to FIG. 98B, a graph of the relationships can be made,although doing so in 2D space is often impossible. In groups G1 and G2above, a representation of a 2-D graph that meets the neighbor criteriamight look like reference numeral 980. Using this grouping method andprocedure, it can be deduced that a group of files are pattern-relatedand are more closely similar to each other, than to files which findmembership in another group. Thus, files F1, F3 and F5 are more closelysimilar than those in group G2.

In order to find relationships or groupings of files in alternateembodiments of the invention, the following proposes an embodiment ofrelevancy groups for arbitrary sets of data files having rightly sizedand rightly numbered files. In turn, underlying data of the files ispartitioned into meaningful groups without any prior classificationschemes or metadata analysis. There is no defining a number of groupsbefore grouping begins and criteria for ascertaining functions forstopping grouping is revealed.

With reference to FIGS. 99A and 99B, a sample of one-hundred files (F1,F2 . . . F100) is prospectively taken, and distance values are obtainedbetween them. In FIG. 99A, the actual distance values are placed into amatrix 450. As between a file and itself, such as between file F1 andF1, or file F100 and F100, a distance value of 0.0 appears in the matrixcells. As between other files, distance values range upward to 70.0.This figure is similar in matrix form to the earlier table labeled“distance matrix.” In FIG. 99B, a matrix 452 of sorted distance valuesis arranged in columns to show a first closest file, then a secondclosest file, and so on until a last or 100^(th) closest file isrevealed for each of the one-hundred files (rows). This view is similarto the table example labeled “sorted distance matrix.”

Generically, skilled artisans create these matrixes as array “distances”that are N×N in an (N) multi-dimensional space. Each Row_(i) in thetable represents file F_(i), each Col_(k) in the table represents fileF_(k), and cell at Row_(i) and Col_(k) in represents the distance fromF_(i) to F_(k). The values in the matrix are generically floating pointvalues, depending on the algorithm used to generate the vectors in theN-dimensional symbol universe. Sometimes they range from 0.0 to 1.0inclusive, or sometimes they range from 1.0 to some MAX value. Eitherembodiment is acceptable for use with the following grouping algorithm.

The “sorted” array is also N×N where each row is sorted from the closestfile (itself) to its furthest neighbor. In this case, each Row_(i) inthe table still represents Fi, but each Col_(k) now represents theK^(th) closest file and thus each cell at Row_(i) and Col_(k) has avalue J that represents F_(j). This means that the value J is in thecell at Row_(i) and Col_(k) then F_(j) is the K^(th) closest file to F₁.

Hereafter, the minimum and maximum distances between any two files inthe “distances” matrix are calculated. In the ongoing example of FIGS.99A and 99B, 0.0 and 70.0 are the minimums and maximums.

Next, a stepping mechanism is created that moves a tolerance value inrounds between the min and max values in some regular fashion. In oneembodiment, this could be a linear progress with (step+1) iterationsusing a formula like (min+((max−min)/round)*(round−1)) for each round instep+1 rounds. Alternatively, this could be a log or exponential typefunction that moves much more slowly for “close” values and much morequickly for large values. The latter type of progress is much moreuseful in multi-dimensional N dimensional symbol universes where somenodes are very far away from a cluster of nodes that are close together.Whatever the stepping function, the tolerance value grows.

A tolerance is calculated (increasing with each round) and a group ofmembers (e.g., files) is determined for each row in the “Distances”matrix 450. Only those files that are closer than or equal to thetolerance value are included in that relevancy group for that file forthat round. For example, consider Row 1 for file F1 in the Distancesmatrix 450 which has ten steps of movement through the minimum andmaximum values (from 0.0 to 70.0) with the tolerance value growing inlinear fashion starting at 0.0 and moving to 70.0 by a tolerance of 7.0at each step for 11 (steps+1) rounds. The result is seen in FIG. 100A.Also, example relevancy groupings include only itself in round 1, sincethe tolerance value is 0.0 (labeled 470). In round 4, on the other hand,four files (F1, F2, F99 and F100) are grouped 472 since each has adistance value closer or equal to a tolerance value of 21.0. Namely,file F1 has a distance value of 0.0, while each of files F2, F99 andF100 have distance values of 10.0, 20.0 and 5.0, respectively, as seenin FIG. 99A. Similarly, Row 3, file F3, from FIG. 99A has groupingsgiven as element 475 in FIG. 100B.

Other rows would follow similar patterns. For any row, skilled artisansshould observe that a relevancy group grows in members as the tolerancesgrow larger as it approaches the MAX value. At each round, any groupsthat are subsets of any other groups are deleted since they add no moreinformation to the set of relevancy groups. Also, at round 1 there areone-hundred separate groups with each file being in its own dedicatedgroup (or one member per one group). This is expected since thetolerance is 0.0 and the group does not include any other files otherthan the file itself since no other files are “closer” than the fileitself. Unfortunately, this set of one-hundred groups with one file isnot interesting from a “relevancy groups” point of view since the numberof relevancy groups is the same as the number of individual files. Theinventors refer to this situation as “isolation” and it represents oneend of the spectrum defining relevancy groups, e.g., one file per groupand the number of groups equals the original number of files, in thiscase 100.

In the middle of grouping, at Round_(x) there are some number of groupssuch that the number of groups is more than one, but less than the totalpossible numbers of groups, or, 1<=NumberGroups(Round_(x))<=100.

In the last round, round 11 or round (steps+1), there is only one groupremaining and it includes all files as members. This is due to the factthat the tolerance has now reached the maximum value of any distance inthe Distances matrix. So, all files are within that closeness to anyother file and each group for each row now includes all files such thatevery group for every row is a subset of each other and they all containall files. Thus, at round 1, there were 100 groups, each with onemember. At the last round, round 11, there is only 1 group with 100files in the group. The inventors call the latter “chaos” or “totalintegration” and it is at the other end of the spectrum definingrelevancy groups. It is opposite the spectrum where “isolation” occurs.Also, this single group of 100 files is also not interesting from a“relevancy groups” point of view since all files are integrated into achaotic mess of only one relevancy group.

As a result, the inventors have valuably identified a situation as towhen the tolerance should stop growing and at which round the groupingshould stop so that the resultant relevancy group is rightly sized withthe right number of groups. The inventors seek to avoid isolation (orlimited grouping) or total integration (or chaos) since neither of theseextremes provides optimization. To answer the question of when a correctnumber of groups occur, the inventors have experimented with varioustypes of actual files and data sets. To date, these include: 100 fairlyrandom text, PDF, MS Office, and Open Office documents; 250 fairlyrandom ASCII short stories; 65 PG files (with various levels ofcompression and color); 75 audio files; and various patent files.

Hereafter, the embodiments of the invention identify at least threesituations in which a stopping function is optimized for stopping theadding of members to a relevancy group. With reference to FIG. 101, afirst step 500 begins grouping files and a second 502 applies a stoppingfunction appropriate for the situation at hand. The stopping functionand its features have been learned through experimentation with theactual files and data sets described.

With reference to graph 510, FIG. 102, consider the number of groups ateach round, such as in FIGS. 100A and 100B. Upon plotting, skilledartisans should determine when the number of groups changessignificantly. Although not exact, this is the point where the number ofgroups becomes “too integrated” and the groups themselves become lessmeaningful.

All of these plots 512, 514, 516, 518, and 520 were obtained from realdata sets (101 files with different symbol counting algorithms) and theyshow the number of groups at each round for 100 rounds. From thebeginning, the plots have 101 groups, while at the end they have but onegroup. In between, the plots reveal different information. In anysituation, however, the generic response is to determine the numbers ofgroups per round, step 530, FIG. 103, determine the curve type of theplotted information, step 532, and apply a stopping function per curvetype, step 534.

In the example of the plotted curve 512, FIG. 102, “Sample 1” shows asmooth “Reverse S” shaped curve. This embodiment contemplates a stoppingpoint for curves shaped like “Sample 1” at the round where the number ofgroups decreases by more than S %, where S % is configurable with anyvalue between 5% and 50% depending on the data set but utilizing adefault value of 10% in the absence of any other configuration data.This is an inflection point that shows larger numbers of files startingto be grouped together and so the groups are becoming more chaotic afterthis point. For “Sample 1,” the stopping point is at round 9. Samples 3,4 and 5, (plots 516, 518, 520) all are similar and they show a gradual,but “bumpy” decrease until there is a sharp increase. This reflects a“local minimum” defined by a jump in the number of groups by 10% ormore. This is a good stopping point since further rounds start to addmany new overlapping groups. For these data sets, and the curves thatlook like these, the stopping point would be at around round 24 or 25.Sample 2 (plot 514), on the other hand, shows a steady decrease in thenumber of groups (which also means there is a steady increase in thenumber of files in each group which is leading to more and more chaos).For curve “Sample 2” there is no clear significant increase until round55. However, if grouping stopped there, the groups would be toointegrated and less meaningful. In this situation, experimental resultshave called for a stopping point at one quarter of the total number ofrounds (which in this case would be at round 25 or 101/4).

In a second approach to applying a stopping function, stopping can occurat a time when there is no overlapping, FIG. 104. For example, considerthe following “transitive closure” on membership that yields trulymutually exclusive groups.

Instead of having these overlapping groups,

{1,2,3}

{1,2,3,4}

{4,5}

{6,7,8}

{8,9}

a re-defining of the groups reveals

{1,2,3, 4,5}

{6,7,8, 9}

In this case, the number of groups reduces much more quickly than incase 1 above and so it is impractical to use a metric like a 10%decrease in a steep “Reverse S” curve or a 10% increase in “localminimum” curves. The stopping point for this type of grouping algorithm,then, would be based on a much larger percent. It is recommended thatstopping occur at the round where only ⅓ (33%) of the original number ofgroups is obtained. These groups are often more broad and not tightlyclustered groups, but the inventors have found that they are good groupsfor making a first level segmentation decision. More fine-grained groupdivisions could then be done amongst each 1st level group, e.g., takinganother third of the first third, and so on.

In a third approach to stopping, a function examines the size of eachgroup and “dismisses a group” when it becomes fairly meaningless.Representatively, FIG. 105 shows this as steps 540 and 542. In oneembodiment, the dismissal occurs by the following example. A controlshows groups whose size is anywhere from 2 members to some percent (say25%) of the total number of members in the original data set. In theongoing example of the 100 files data-set, numbers of groups having from2 to 25 members are examined. Once the membership gets so large, thegroup becomes “noise” and is not meaningful any more. The max size ofthe groups that are not dismissed can range anywhere from 20% to 50%based on the data set. This embodiment calls for a variable percent thatcan be manipulated for a “soft” stopping point. Once there are no moregroups that fit the criteria for not being dismissed, adding groups isstopped.

Among certain advantages of the foregoing stopping approaches is that aright number and right sized relevancy group for an arbitrary set ofdata files is readily determined. These relevancy groups are then usedto partition the data into meaningful groups without any priorclassification or metadata analysis. This also occurs according to thefollowing: without any pre-defined or pre-declared conditions about thenumber or size of the groups; by organizing relevance groups into humanunderstandable relevance relationships without any human intervention;and by optimally combining related files into relevance groups up to apoint but not passing the point where the relevance groups become toobroad to be useful.

The foregoing has been described in terms of specific embodiments, butone of ordinary skill in the art will recognize that additionalembodiments are possible without departing from its teachings. Thisdetailed description, therefore, and particularly the specific detailsof the exemplary embodiments disclosed, is given primarily for clarityof understanding, and no unnecessary limitations are to be implied, formodifications will become evident to those skilled in the art uponreading this disclosure and may be made without departing from thespirit or scope of the invention. Relatively apparent modifications, ofcourse, include combining the various features of one or more figureswith the features of one or more of the other figures.

The invention claimed is:
 1. In a computing system environment, a methodof differentiating files stored on one or more computing devices,comprising: over a sequence of rounds, grouping together filescompressed according to an original relationship of highly occurringpatterns in all bits of binary data of the uncompressed data of thefiles without any prior classification scheme nor metadata analysis ofsaid files, the original relationship including a distance value betweensaid compressed files in a multi-dimensional space; determining atolerance value for the sequence of rounds based on a minimum and amaximum said distance value; and applying a stopping function to thegrouping together.
 2. The method of claim 1, further includingdetermining a relationship between numbers of groups per each round ofthe sequence of rounds.
 3. The method of claim 2, wherein therelationship between the numbers of groups per said each round includesa curve and the applying the stopping function occurs relative to anidentified type of said curve.
 4. The method of claim 2, furtherincluding determining a decrease in the numbers of groups per said eachround.
 5. The method of claim 4, wherein the applying the stoppingfunction occurs when the decrease is about 5% to 50% relative to anearlier round of the sequence of rounds.
 6. The method of claim 2,further including determining a local minimum in the numbers of groupsper said each round.
 7. The method of claim 6, wherein the applying thestopping function occurs upon reaching the local minimum.
 8. The methodof claim 1, further including determining a total number of rounds ofthe sequence of rounds, wherein the applying the stopping functionoccurs at about one fourth of the determined total number of rounds. 9.The method of claim 1, further including applying a linear orexponential stepping function.
 10. In a computing system environment, amethod of differentiating files stored on one or more computing devices,comprising: over a sequence of rounds, grouping together filescompressed according to an original relationship of highly occurringpatterns in all bits of binary data of uncompressed data of the fileswithout any prior classification scheme nor metadata analysis of saidfiles, the original relationship including a distance value between saidcompressed files in a multi-dimensional space; determining a tolerancevalue for the sequence of rounds based on a minimum and a maximum saiddistance value; and applying a stopping function to the groupingtogether to obtain rightly sized pluralities of file groups.
 11. Themethod of claim 10, wherein the applying the stopping function occurswhen individual groups of the pluralities of file groups have nooverlapping members of files.
 12. The method of claim 11, furtherincluding redefining at least two said individual groups initiallyhaving overlapping members of files to be mutually exclusive in membersof files.
 13. The method of claim 10, further including applying thestopping function upon reaching a predetermined decrease in numbers ofgroups from an original number of groups of the pluralities of filegroups.
 14. In a computing system environment, a method ofdifferentiating files stored on one or more computing devices,comprising: over a sequence of rounds, grouping together filescompressed according to an original relationship of highly occurringpatterns in all bits of binary data of uncompressed data of the fileswithout any prior classification scheme nor metadata analysis of saidfiles, the original relationship including a distance value between saidcompressed files in a multi-dimensional space; determining a tolerancevalue for the sequence of rounds based on a minimum and a maximum saiddistance value; and applying a stopping function to the groupingtogether to obtain rightly sized pluralities of file groups havingmembers of files below a predetermined numerical threshold.
 15. Themethod of claim 14, further including determining a size of said membersof files for each of said file groups.
 16. The method of claim 14,further including applying the stopping function upon reaching thepredetermined numerical threshold.
 17. The method of claim 14, furtherincluding applying the stopping function upon said members of files ineach of said file groups reaching about one fourth or less of a maximumnumber of original file groups.
 18. The method of claim 14, furtheringincluding dismissing any of said file groups having members of filesabove the predetermined numerical threshold.